Compression and Decompression in Mathematics
Danesi, Marcel, editor. 2020. Interdisciplinary Perspectives on Math Cognition. Chapter 2. Springer.
24 Pages Posted: 10 Jul 2019
Date Written: July 7, 2019
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.
Keywords: mathematics, cognition, conceptual blending
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