Functorial semiotics for creativity in music and mathematics / Guerino Mazzola, Sangeeta Dey, Zilu Chen, Yan Pang.
2022
ML3800
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Details
Title
Functorial semiotics for creativity in music and mathematics / Guerino Mazzola, Sangeeta Dey, Zilu Chen, Yan Pang.
ISBN
9783030851903 (electronic bk.)
3030851907 (electronic bk.)
9783030851897
3030851893
3030851907 (electronic bk.)
9783030851897
3030851893
Published
Cham, Switzerland : Springer, 2022.
Language
English
Description
1 online resource (1 volume) : illustrations (black and white, and colour).
Item Number
10.1007/978-3-030-85190-3 doi
Call Number
ML3800
Dewey Decimal Classification
780/.0519
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Computational music science.
Available in Other Form
Functorial semiotics for creativity in music and mathematics.
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Table of Contents
Part I Orientation
Part II General Concepts
Part III Semantic Math
Part IV Applications
Part V Conclusions
References
Index.
Part II General Concepts
Part III Semantic Math
Part IV Applications
Part V Conclusions
References
Index.