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Functorial Semiotics for Creativity in Music and Mathematics
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Functorial Semiotics for Creativity in Music and Mathematics/ by Guerino Mazzola, Sangeeta Dey, Zilu Chen, Yan Pang.
作者:
Mazzola, Guerino.
其他作者:
Pang, Yan.
面頁冊數:
XIII, 166 p.online resource. :
Contained By:
Springer Nature eBook
標題:
Computational Mathematics and Numerical Analysis. -
電子資源:
https://doi.org/10.1007/978-3-030-85190-3
ISBN:
9783030851903
Functorial Semiotics for Creativity in Music and Mathematics
Mazzola, Guerino.
Functorial Semiotics for Creativity in Music and Mathematics
[electronic resource] /by Guerino Mazzola, Sangeeta Dey, Zilu Chen, Yan Pang. - 1st ed. 2022. - XIII, 166 p.online resource. - 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 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.
ISBN: 9783030851903
Standard No.: 10.1007/978-3-030-85190-3doiSubjects--Topical Terms:
669338
Computational Mathematics and Numerical Analysis.
LC Class. No.: T57-57.97
Dewey Class. No.: 780.0519
Functorial Semiotics for Creativity in Music and Mathematics
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