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A Cognitive and Quantitative Approach to Mathematical Concretization

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Abstract

This chapter analyses the linguistic role of analogy as a strategy of concretizing abstract concepts addressed in popular science focused on mathematics. A rich analogy used in a text popularising number theory is explored through firstly a quantitative method and then using conceptual blending, a theory taken from cognitive linguistics. The chapter demonstrates the use of corpus-based and cognitive approaches to language in the analysis of the ways in which popular science texts aim to give non-experts a sense of understanding of complex mathematical concepts.

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Works cited

  • Abbott, Edwin A. 1884. Flatland: A Romance in Many Dimensions. London: Seely and Co.

    Google Scholar 

  • Alexander, Marc and Fraser Dallachy. 2020. “Lexis”. In The Routledge Handbook of English Language and Digital Humanities, edited by Svenja Adolphs and Dawn Knight. London: Routledge. 164-84.

    Google Scholar 

  • Alexander, Marc, Fraser Dallachy, Scott Piao, Alistair Baron and Paul Rayson. 2015. “Metaphor, Popular Science, and Semantic Tagging: Distant Reading with the Historical Thesaurus of English.Digital Scholarship in the Humanities 30 (s1): i16–i27.

    Google Scholar 

  • Baayen, R. Harald. 2008. Analyzing Linguistic Data. A Practical Introduction to Statistics Using R. Cambridge: Cambridge University Press.

    Google Scholar 

  • Baker, Paul. 2010. Sociolinguistics and Corpus Linguistics. Edinburgh: Edinburgh University Press.

    Google Scholar 

  • Bird, Steven, Ewan Klein, and Edward Loper. 2009. Natural Language Processing with Python. Sebastopol, CA: O’Reilly.

    Google Scholar 

  • Burrows, John F. 1992. “Not Unless You Ask Nicely: The Interpretative Nexus between Analysis and Information”. Literary and Linguistic Computing 7: 91–109.

    Google Scholar 

  • Coppel, William A. 2009. Number Theory: An Introduction to Mathematics, 2nd ed. London: Springer.

    Book  Google Scholar 

  • Coulson, Seana. 2001. Semantic Leaps: Frame-shifting and Conceptual Blending in Meaning Construction. New York: Cambridge University Press.

    Book  Google Scholar 

  • Coulson, Seana and Todd Oakley. 2000. “Blending Basics”. Cognitive Linguistics 11 (3–4): 175–96.

    Google Scholar 

  • Dunning, Ted. 1993. “Accurate Methods for the Statistics of Surprise and Coincidence”. Computational Linguistics 19: 61–74.

    Google Scholar 

  • du Sautoy, Marcus. 2003. The Music of the Primes: Why an Unsolved Problem in Mathematics Matters. London: Harper Perennial.

    Google Scholar 

  • Fauconnier, Gilles and George Lakoff. 2010. On Metaphor and Blending. http://www.cogsci.ucsd.edu/~coulson/spaces/GG-final-1.pdf (1 August 2019).

  • Fauconnier, Gilles and Mark Turner. 1998. “Conceptual Integration Networks”. Cognitive Science 22: 133–87.

    Google Scholar 

  • ———. 2002. The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities. New York: Basic Books.

    Google Scholar 

  • Gibbs, Raymond W. 2006. “Introspection and Cognitive Linguistics: Should We Trust Our Own Intuitions?” Annual Review of Cognitive Linguistics 4: 135–51.

    Google Scholar 

  • Kay, Christian, Marc Alexander, Fraser Dallachy, Jane Roberts, Michael Samuels and Irené Wotherspoon (eds.). 2019. The Historical Thesaurus of English, version 4.21. https://ht.ac.uk/.

  • Lakoff, George. 1993. “The Contemporary Theory of Metaphor”. In Metaphor and Thought, edited by Andrew Ortony, 2nd ed. Cambridge: Cambridge University Press. 202–51.

    Google Scholar 

  • Lakoff, George, and Mark Johnson. 1980. Metaphors We Live By. Chicago: University of Chicago Press.

    Google Scholar 

  • Lakoff, George, and Rafael Nuñez. 2000. Where Mathematics Comes From. New York: Basic Books.

    Google Scholar 

  • Larose, Daniel. 2006. Data Mining Methods and Models. Hoboken, NJ: Wiley.

    Google Scholar 

  • Leech, Geoffrey, and Mick Short. 1981. Style in Fiction: A Linguistic Introduction to English Fictional Prose. London: Longman.

    Google Scholar 

  • McIntyre, Dan and Brian Walker. 2010. “How Can Corpora be Used to Explore the Language of Poetry and Drama?” In The Routledge Handbook of Corpus Linguistics, edited by Anne O’Keeffe and Michael McCarthy. London: Routledge. 516–30.

    Google Scholar 

  • Mazur, Barry. 2004. Imagining Numbers: Particularly the Square Root of Minus Fifteen. Harmondsworth: Penguin.

    Google Scholar 

  • Mendenhall, T. C. 1887. “The Characteristic Curves of Composition”. Science IX (214). 237-248.

    Google Scholar 

  • ———. 1901. “A Mechanical Solution of a Literary Problem”. Popular Science Monthly LX (7): 97–105.

    Google Scholar 

  • Mendoza-Denton, Norma, Jennifer Hay, and Stefanie Jannedy. 2003. “Probabilistic Sociolinguistics: Beyond Variable Rules”. In Probabilistic Linguistics, edited by Rens Bod, Jennifer Hay, and Stefanie Jannedy, 97–138. Cambridge, MA: MIT Press.

    Google Scholar 

  • Piao, Scott, Fraser Dallachy, Alistair Baron, Jane Demmen, Stephen Wattam, Philip Durkin, James McCracken, Paul Rayson and Marc Alexander. 2017. “A Time-sensitive Historical Thesaurus-based Semantic Tagger for Deep Semantic Annotation.” Computer Speech and Language 46: 113–35.

    Google Scholar 

  • Rayson, Paul, Damon Berridge, and Brian Francis. 2004. “Extending the Cochran Rule for the Comparison of Word Frequencies between Corpora”. 7th International Conference on Statistical Analysis of Textual Data. http://eprints.comp.lancs.ac.uk/893/ (5 August 2019).

  • Rozenfeld, Boris Abramovich. 1988. A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space. London: Springer.

    Book  Google Scholar 

  • Selisker, Scott. 2012. “The Digital Inhumanities?”. Los Angeles Review of Books, 5 November 2012. https://lareviewofbooks.org/essay/in-defense-of-data-responses-to-stephen-marches-literature-is-not-data.

  • Sinclair, John M. 2007. “The Exploitation of Meaning: Literary Text and Local Grammars”. In Challenging the Boundaries, edited by Isil Bas & Donald C. Freeman, 1−36. Amsterdam: Rodopi.

    Google Scholar 

  • Terras, Melissa, Julianne Nyhan, and Edward Vanhoutte. 2013. Defining Digital Humanities: A Reader. Farnham: Ashgate.

    Google Scholar 

  • Underwood, Ted. 2017. “A Genealogy of Distant Reading”. Digital Humanities Quarterly (online) 11 (2).

    Google Scholar 

  • Ungerer, Friedrich, and Hans-Jorg Schmid. 2006. An Introduction To Cognitive Linguistics, 2nd ed. Harlow: Longman.

    Google Scholar 

  • Woźny, Jacek. 2018. How We Understand Mathematics: Conceptual Integration in the Language of Mathematical Description. New York: Springer.

    Book  Google Scholar 

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Alexander, M. (2021). A Cognitive and Quantitative Approach to Mathematical Concretization. In: Tubbs, R., Jenkins, A., Engelhardt, N. (eds) The Palgrave Handbook of Literature and Mathematics. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-55478-1_32

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