Abstract
Since antiquity, it has been recognized that the human body and brain are small, local, and limited. Working memory is equally limited. How can immense ranges of meaning be managed within the limits of the processes of thought? Blending is a conceptual operation that helps to make intractable mental networks tractable. Blending can operate on large networks of mental spaces to produce tight, conceptually congenial, compressed blended spaces. These compressed blended spaces can then serve as manageable platforms for thinking. Working from the congenial blend, the mind can extend to this or that part of a mental network that would otherwise be too large, complex, and capacious to handle. Such mental acts of compression and decompression are essential tools of mathematical thinking and mathematical invention. This article analyzes patterns of compression and decompression in mathematics.
This chapter is based on chapters in Turner, M. (2014). The Origin of Ideas: Blending, Creativity, and the Human Spark. New York: Oxford University Press.
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References
Alexander, J. (2011). Blending in mathematics. Semiotica, 187): 1–48. ISSN (Online) 1613-3692, ISSN (Print) 0037-1998, doi: https://doi.org/10.1515/semi.2011.063.
Dehaene, S., Izard, V., Spelke, E., and Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in western and Amazonian indigene cultures. Science 320: 1217–1220.
Núñez, Rafael. (2011). No innate number line in the human brain. Journal of Cross-Cultural Psychology 42(4): 651–668.
Pagán Cánovas, C. (2011). The genesis of the arrows of love: diachronic conceptual integration in Greek mythology. American Journal of Philology 132(4): 553–579.
Pagán Cánovas, C. and Turner, M. (2016). Generic integration templates for fictive communication. In: E. Pascual and S. Sandler (eds.), The conversation frame: Forms and functions of fictive interaction, pp. 45–62. Amsterdam: John Benjamins.
Philo (called Judæus or “of Alexandria”). (1854–1890). On the principle that the worse is accustomed to be always plotting against the better, (Quod Deterius Potiori Insidiari Soleat), chapter 7 of Yonge, Charles Duke, translator, The works of Philo Judæus. London: H. G. Bohn.
Turner, M. (1991). Reading minds: The study of English in the age of cognitive science. Princeton: Princeton University Press.
Turner, M. (2014). The Origin of Ideas: Blending, Creativity, and the Human Spark. New York: Oxford University Press.
Weyl, H. (1952). Symmetry. Princeton: Princeton University Press.
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Turner, M. (2019). Compression and Decompression in Mathematics1. In: Danesi, M. (eds) Interdisciplinary Perspectives on Math Cognition. Mathematics in Mind. Springer, Cham. https://doi.org/10.1007/978-3-030-22537-7_2
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DOI: https://doi.org/10.1007/978-3-030-22537-7_2
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