Authors:
- The first functorial semiotic theory for creativity in music and mathematics
- Application of topos theory to the classification of creativity
- Proposes object-oriented schemes for software implementation of AI of creativity
Part of the book series: Computational Music Science (CMS)
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Table of contents (12 chapters)
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Front Matter
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Orientation
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Front Matter
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General Concepts
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Front Matter
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Semantic Math
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Front Matter
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Applications and Consequences
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Front Matter
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References, Index
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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School of Music, University of Minnesota, Minneapolis, USA
Guerino Mazzola, Sangeeta Dey
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New York University, New York, USA
Zilu Chen
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School of Music, Yan Pang Create, LLC, Minneapolis, USA
Yan Pang
Bibliographic Information
Book Title: Functorial Semiotics for Creativity in Music and Mathematics
Authors: Guerino Mazzola, Sangeeta Dey, Zilu Chen, Yan Pang
Series Title: Computational Music Science
DOI: https://doi.org/10.1007/978-3-030-85190-3
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-030-85189-7Published: 24 April 2022
Softcover ISBN: 978-3-030-85192-7Published: 24 April 2023
eBook ISBN: 978-3-030-85190-3Published: 23 April 2022
Series ISSN: 1868-0305
Series E-ISSN: 1868-0313
Edition Number: 1
Number of Pages: XIII, 166
Topics: Mathematics in Music, Semiotics, Neurosciences, Creativity and Arts Education, Artificial Intelligence, Computational Mathematics and Numerical Analysis