Functorial Semiotics for Creativity in Music and Mathematics
English | 2022 | ISBN: 3030851893 | 165 Pages | PDF | 6 MB
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.
home page:
https://amzn.to/3MqyLdI
DOWNLOAD
Related News:
Making Musical Time by Guerino MazzolaEnglish | 2021 | ISBN: 978-3-030-85629-8 | 265 pages | PDF | 10 MB This book is a comprehensive examination of the conception, perception, performance, and composition of time in music across time and culture. It surveys the literature of time in mathematics, philosophy, psychology, music theory, and somatic studies (medicine and disability studies) and looks ahead through original research in...
Let’s Calculate Bach: Applying Information Theory and Statistics to Numbers in MusicEnglish | 2021 | ISBN: 3030637689 | 372 pages | pdf, epub | 49 MB This book shows how information theory, probability, statistics, mathematics and personal computers can be applied to the exploration of numbers and proportions in music. It brings the methods of scientific and quantitative thinking to questions like: What are the ways of encoding a message in music and how can we be sure of the...
The Future of Music: Towards a Computational Musical Theory of EverythingEnglish | ISBN: 3030397084 | 2020 | 257 pages | EPUB: 42 MB | PDF: 5 MB The idea of this monograph is to present an overview of decisive theoretical, computational, technological, aesthetical, artistic, economical, and sociological directions to create future music. It features a unique insight into dominant scientific and artistic new directions, which are guaranteed by the authors`...
The Topos of Music I: Theory: Geometric Logic Classification Harmony Counterpoint Motives Rhythm vol 2English | ISBN: 3319643630 | 2017 | 656 pages | PDF | 43.16 MB This is the first volume of the second edition of the now classic book “The Topos of Music”. The author explains the theory`s conceptual framework of denotators and forms, the classification of local and global musical objects, the mathematical models of harmony and counterpoint, and topologies for rhythm and motives....
Comments for Functorial Semiotics for Creativity in Music and Mathematics:
No comments yet, add a comment!