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Functorial Semiotics for Creativity in Music and Mathematics 2021 Edition
Contributor(s): Mazzola, Guerino (Author), Dey, Sangeeta (Author), Chen, Zilu (Author)
ISBN: 3030851893     ISBN-13: 9783030851897
Publisher: Springer
OUR PRICE:   $123.49  
Product Type: Hardcover
Published: April 2022
Qty:
Temporarily out of stock - Will ship within 2 to 5 weeks
Additional Information
BISAC Categories:
- Mathematics | Applied
- Literary Criticism | Semiotics & Theory
- Medical | Neuroscience
Physical Information: 0.63" H x 8.19" W x 11.1" (1.35 lbs) 166 pages
 
Descriptions, Reviews, Etc.
Publisher Description:

This book presents a new semiotic theory based upon category/topos theory, and applied to a classification (three types) of creativity in music and mathematics. The purpose is a first functorial approach to a mathematical semiotics that will be applied to AI implementations for creativity. It is the only semiotic approach to creativity in music and mathematics that uses 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) parametrizes semiotic units and enables a Čech cohomology of manifolds of semiotic entities. It opens up a conceptual mathematics as initiated by Grothendieck and Galois. It enables 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 readers 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.