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Functorial Semiotics for Creativity in Music and Mathematics (Hardcover, 1st ed. 2022)
Loot Price: R3,171
Discovery Miles 31 710
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Functorial Semiotics for Creativity in Music and Mathematics (Hardcover, 1st ed. 2022)
Series: Computational Music Science
Expected to ship within 12 - 17 working days
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This book presents a new semiotic theory based upon category theory
and applying to a classification of creativity in music and
mathematics. It is the first functorial approach to mathematical
semiotics that can be applied to AI implementations for creativity
by using topos theory and its applications to music theory. Of
particular interest is the generalized Yoneda embedding in the
bidual of the category of categories (Lawvere) - parametrizing
semiotic units - enabling a Cech cohomology of manifolds of
semiotic entities. It opens up a conceptual mathematics as
initiated by Grothendieck and Galois and allows a precise
description of musical and mathematical creativity, including a
classification thereof in three types. This approach is new, as it
connects topos theory, semiotics, creativity theory, and AI
objectives for a missing link to HI (Human Intelligence). The
reader can apply creativity research using our classification,
cohomology theory, generalized Yoneda embedding, and Java
implementation of the presented functorial display of semiotics,
especially generalizing the Hjelmslev architecture. The intended
audience are academic, industrial, and artistic researchers in
creativity.
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