國立虎尾科技大學 |

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
LDR:02840nam a22004455i 4500 001 1093175
003 DE-He213
005 20220423094647.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783030851903 $9 978-3-030-85190-3
024 7 $a 10.1007/978-3-030-85190-3 $2 doi
035 $a 978-3-030-85190-3
050 4 $a T57-57.97
050 4 $a ML1-3930
072 7 $a PBW $2 bicssc
072 7 $a AVA $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBW $2 thema
072 7 $a AVA $2 thema
082 0 4 $a 780.0519 $2 23
100 1 $a Mazzola, Guerino. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 670247
245 1 0 $a Functorial Semiotics for Creativity in Music and Mathematics $h [electronic resource] / $c by Guerino Mazzola, Sangeeta Dey, Zilu Chen, Yan Pang.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XIII, 166 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 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.
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 669338
650 2 4 $a Artificial Intelligence. $3 646849
650 2 4 $a Creativity and Arts Education. $3 1113649
650 2 4 $a Computational Neuroscience. $3 1390780
650 1 4 $a Mathematics in Music. $3 885668
650 0 $a Mathematics—Data processing. $3 1365953
650 0 $a Artificial intelligence. $3 559380
650 0 $a Art—Study and teaching. $3 1366158
650 0 $a Computational neuroscience. $3 581378
650 0 $a Semiotics. $3 559892
650 0 $a Music—Mathematics. $3 1391329
700 1 $a Pang, Yan. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1114510
700 1 $a Chen, Zilu. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1283247
700 1 $a Dey, Sangeeta. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1362568
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030851897
776 0 8 $i Printed edition: $z 9783030851910
776 0 8 $i Printed edition: $z 9783030851927
830 0 $a Computational Music Science, $x 1868-0305 $3 1261929
856 4 0 $u https://doi.org/10.1007/978-3-030-85190-3
912 $a ZDB-2-SCS
912 $a ZDB-2-SXCS
950 $a Computer Science (SpringerNature-11645)
950 $a Computer Science (R0) (SpringerNature-43710)