Functorial Semiotics for Creativity in Music and Mathematics / by Guerino Mazzola, Sangeeta Dey, Zilu Chen, Yan Pang
(Computational Music Science. ISSN:18680313)
データ種別 | 電子ブック |
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版 | 1st ed. 2022. |
出版者 | (Cham : Springer International Publishing : Imprint: Springer) |
出版年 | 2022 |
大きさ | XIII, 166 p : online resource |
著者標目 | *Mazzola, Guerino author Dey, Sangeeta author Chen, Zilu author Pang, Yan author SpringerLink (Online service) |
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一般注記 | 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 HTTP:URL=https://doi.org/10.1007/978-3-030-85190-3 |
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件 名 | LCSH:Music -- Mathematics
全ての件名で検索
LCSH:Semiotics LCSH:Computational neuroscience LCSH:Art -- Study and teaching 全ての件名で検索 LCSH:Artificial intelligence LCSH:Mathematics -- Data processing 全ての件名で検索 FREE:Mathematics in Music FREE:Semiotics FREE:Computational Neuroscience FREE:Creativity and Arts Education FREE:Artificial Intelligence FREE:Computational Mathematics and Numerical Analysis |
分 類 | LCC:T57-57.97 LCC:ML1-3930 DC23:780.0519 |
書誌ID | EB00002260 |
ISBN | 9783030851903 |
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