Functorial Semiotics for Creativity in Music and Mathematics

This book presents a new semiotic theory based on category theory and applies 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, using topos theory and its applications to music theory. 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. The intended audience are academic, industrial, and artistic researchers in creativity.

Format: Paperback / softback
Length: 166 pages
Publication date: 24 April 2023
Publisher: Springer Nature Switzerland AG

This groundbreaking book presents a novel semiotic theory rooted in category theory, which applies to the classification of creativity in music and mathematics. It stands as the pioneering functorial approach to mathematical semiotics, making it highly applicable to AI implementations for creativity, leveraging topos theory and its applications in music theory.

One of the key aspects of this work is the generalized Yoneda embedding in the bidual of the category of categories (Lawvere) - parametrizing semiotic units - which enables the study of Čech cohomology of manifolds of semiotic entities. This groundbreaking development opens up a realm of conceptual mathematics, akin to the pioneering work of Grothendieck and Galois. It provides a precise framework for describing musical and mathematical creativity, encompassing a comprehensive classification of these creative processes into three distinct types.

What sets this approach apart is its unique fusion of topos theory, semiotics, creativity theory, and AI objectives. It seeks to bridge the gap between these diverse fields, providing a missing link to the realm of human intelligence (HI). By applying the classification, cohomology theory, generalized Yoneda embedding, and Java implementation of the presented functorial display of semiotics, researchers in academia, industry, and the arts can delve into creativity research with greater precision and effectiveness.

The intended audience for this book encompasses academic, industrial, and artistic researchers who are passionate about exploring the intricacies of creativity. Whether they are experts in mathematics, music, semiotics, or AI, this comprehensive resource offers valuable insights and tools for advancing their understanding and applications in this field.

Weight: 458g
Dimension: 279 x 210 (mm)
ISBN-13: 9783030851927
Edition number: 1st ed. 2022