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Interdisciplinary Perspectives on Math CognitionCompression and Decompression in Mathematics1

Interdisciplinary Perspectives on Math Cognition: Compression and Decompression in Mathematics1 [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Interdisciplinary Perspectives on Math CognitionCompression and Decompression in Mathematics1

Part of the Mathematics in Mind Book Series
Editors: Danesi, Marcel
Turner, Mark
Interdisciplinary Perspectives on Math Cognition — Sep 15, 2019
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References (12)

Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2019
ISBN
978-3-030-22536-0
Pages
29 –51
DOI
10.1007/978-3-030-22537-7_2
Publisher site
See Chapter on Publisher Site

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.]

Published: Sep 15, 2019

Keywords: Origin of mathematical concepts; Compression and decompression; Conceptual blending; Analogies; Disanalogies

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