Functorial Semiotics for Creativity in Music and Mathematics

Guerino Mazzola, Sangeeta Dey, Zilu Chen , Yan Pang

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English

Springer Nature Switzerland AG
24 April 2023

Theory of music & musicology; Semiotics & semiology; Teaching of a specific subject; Applied mathematics; Neurosciences; Artificial intelligence

Series: Computational Music Science

Summary
Details

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 Čech 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.

By: Guerino Mazzola, Sangeeta Dey, Zilu Chen, Yan Pang
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 2022 ed.
Dimensions: Height: 279mm, Width: 210mm,
Weight: 458g
ISBN: 9783030851927
ISBN 10: 3030851923
Series: Computational Music Science
Pages: 166
Publication Date: 24 April 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active