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Functorial semiotics for creativity ...

Mazzola, G.

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Functorial semiotics for creativity in music and mathematics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Functorial semiotics for creativity in music and mathematics/ by Guerino Mazzola ... [et al.].
other author:	Mazzola, G.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xiii, 166 p. :ill., digital ;24 cm.
[NT 15003449]:	Part I Orientation -- Part II General Concepts -- Part III Semantic Math -- Part IV Applications -- Part V Conclusions -- References -- Index.
Contained By:	Springer Nature eBook
Subject:	Music - Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-030-85190-3
ISBN:	9783030851903

Functorial semiotics for creativity in music and mathematics
Functorial semiotics for creativity in music and mathematics[electronic resource] /by Guerino Mazzola ... [et al.]. - Cham :Springer International Publishing :2022. - xiii, 166 p. :ill., digital ;24 cm. - Computational music science,1868-0313. - Computational music science..

Part I Orientation -- Part II General Concepts -- Part III Semantic Math -- Part IV Applications -- Part V Conclusions -- References -- Index.

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.

ISBN: 9783030851903

Standard No.: 10.1007/978-3-030-85190-3doiSubjects--Topical Terms:

2179507
Music
--Mathematics.

LC Class. No.: ML3800

Dewey Class. No.: 780.0519

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245 0 0 $a Functorial semiotics for creativity in music and mathematics $h [electronic resource] / $c by Guerino Mazzola ... [et al.].
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490 1 $a Computational music science, $x 1868-0313
505 0 $a Part I Orientation -- Part II General Concepts -- Part III Semantic Math -- Part IV Applications -- Part V Conclusions -- References -- Index.
520 $a 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.
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