Functorial Semiotics for Creativity in Music and Mathematics

Functorial Semiotics for Creativity in Music and Mathematics

Author: Guerino Mazzola

Publisher: Springer Nature

Published: 2022-04-23

Total Pages: 166

ISBN-13: 3030851907

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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.


Book Synopsis Functorial Semiotics for Creativity in Music and Mathematics by : Guerino Mazzola

Download or read book Functorial Semiotics for Creativity in Music and Mathematics written by Guerino Mazzola and published by Springer Nature. This book was released on 2022-04-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Musical Creativity

Musical Creativity

Author: Guerino Mazzola

Publisher: Springer Science & Business Media

Published: 2011-11-03

Total Pages: 331

ISBN-13: 364224517X

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This book represents a new approach to musical creativity, dealing with the semiotics, mathematical principles, and software for creativity processes. After a thorough introduction, the book offers a first practical part with a detailed tutorial for students in composition and improvisation, using musical instruments and music software. The second, theoretical part deals with historical, actual, and new principles of creative processes in music, based on the results and methods developed in the first author’s book Topos of Music and referring to semiotics, predicative objects, topos theory, and object-oriented concept architectures. The third part of the book details four case studies in musical creativity, including an analysis of the six variations of Beethoven's sonata op. 109, a discussion of the creative process in a CD coproduced in 2011 by the first and second authors, a recomposition of Boulez’s "Structures pour deux pianos" using the Rubato software module BigBang developed by the third author, and the Escher theorem from mathematical gesture theory in music. This is both a textbook addressed to undergraduate and graduate students of music composition and improvisation, and also a state-of-the-art survey addressed to researchers in creativity studies and music technology. The book contains summaries and end-of-chapter questions, and the authors have used the book as the main reference to teach an undergraduate creativity studies program and also to teach composition. The text is supported throughout with musical score examples.


Book Synopsis Musical Creativity by : Guerino Mazzola

Download or read book Musical Creativity written by Guerino Mazzola and published by Springer Science & Business Media. This book was released on 2011-11-03 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents a new approach to musical creativity, dealing with the semiotics, mathematical principles, and software for creativity processes. After a thorough introduction, the book offers a first practical part with a detailed tutorial for students in composition and improvisation, using musical instruments and music software. The second, theoretical part deals with historical, actual, and new principles of creative processes in music, based on the results and methods developed in the first author’s book Topos of Music and referring to semiotics, predicative objects, topos theory, and object-oriented concept architectures. The third part of the book details four case studies in musical creativity, including an analysis of the six variations of Beethoven's sonata op. 109, a discussion of the creative process in a CD coproduced in 2011 by the first and second authors, a recomposition of Boulez’s "Structures pour deux pianos" using the Rubato software module BigBang developed by the third author, and the Escher theorem from mathematical gesture theory in music. This is both a textbook addressed to undergraduate and graduate students of music composition and improvisation, and also a state-of-the-art survey addressed to researchers in creativity studies and music technology. The book contains summaries and end-of-chapter questions, and the authors have used the book as the main reference to teach an undergraduate creativity studies program and also to teach composition. The text is supported throughout with musical score examples.

The Topos of Music IV: Roots

The Topos of Music IV: Roots

Author: Guerino Mazzola

Publisher: Springer

Published: 2018-03-29

Total Pages: 325

ISBN-13: 3319644955

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This is the fourth volume of the second edition of the now classic book “The Topos of Music”. The author presents appendices with background material on sound and auditory physiology; mathematical basics such as sets, relations, transformations, algebraic geometry, and categories; complements in physics, including a discussion on string theory; and tables with chord classes and modulation steps.


Book Synopsis The Topos of Music IV: Roots by : Guerino Mazzola

Download or read book The Topos of Music IV: Roots written by Guerino Mazzola and published by Springer. This book was released on 2018-03-29 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth volume of the second edition of the now classic book “The Topos of Music”. The author presents appendices with background material on sound and auditory physiology; mathematical basics such as sets, relations, transformations, algebraic geometry, and categories; complements in physics, including a discussion on string theory; and tables with chord classes and modulation steps.

Mathematics and Computation in Music

Mathematics and Computation in Music

Author: Jason Yust

Publisher: Springer

Published: 2013-06-05

Total Pages: 256

ISBN-13: 3642393578

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This book constitutes the thoroughly refereed proceedings of the Fourth International Conference on Mathematics and Computation in Music, MCM 2013, held in Montreal, Canada, in June 2013. The 18 papers presented were carefully reviewed and selected from numerous submissions. They are promoting the collaboration and exchange of ideas among researchers in music theory, mathematics, computer science, musicology, cognition and other related fields.


Book Synopsis Mathematics and Computation in Music by : Jason Yust

Download or read book Mathematics and Computation in Music written by Jason Yust and published by Springer. This book was released on 2013-06-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed proceedings of the Fourth International Conference on Mathematics and Computation in Music, MCM 2013, held in Montreal, Canada, in June 2013. The 18 papers presented were carefully reviewed and selected from numerous submissions. They are promoting the collaboration and exchange of ideas among researchers in music theory, mathematics, computer science, musicology, cognition and other related fields.

Making Musical Time

Making Musical Time

Author: Guerino Mazzola

Publisher: Springer Nature

Published: 2021-11-15

Total Pages: 265

ISBN-13: 3030856291

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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 performance, composition, psychology, and education. It is the first monograph solely devoted to the theory of construction of musical time since Kramer in 1988, with new insights, mathematical precision, and an expansive global and historical context. The mathematical methods applied for the construction of musical time are totally new. They relate to category theory (projective limits) and the mathematical theory of gestures. These methods and results extend the music theory of time but also apply to the applied performative understanding of making music. In addition, it is the very first approach to a constructive theory of time, deduced from the recent theory of musical gestures and their categories. Making Musical Time is intended for a wide audience of scholars with interest in music. These include mathematicians, music theorists, (ethno)musicologists, music psychologists / educators / therapists, music performers, philosophers of music, audiologists, and acousticians.


Book Synopsis Making Musical Time by : Guerino Mazzola

Download or read book Making Musical Time written by Guerino Mazzola and published by Springer Nature. This book was released on 2021-11-15 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 performance, composition, psychology, and education. It is the first monograph solely devoted to the theory of construction of musical time since Kramer in 1988, with new insights, mathematical precision, and an expansive global and historical context. The mathematical methods applied for the construction of musical time are totally new. They relate to category theory (projective limits) and the mathematical theory of gestures. These methods and results extend the music theory of time but also apply to the applied performative understanding of making music. In addition, it is the very first approach to a constructive theory of time, deduced from the recent theory of musical gestures and their categories. Making Musical Time is intended for a wide audience of scholars with interest in music. These include mathematicians, music theorists, (ethno)musicologists, music psychologists / educators / therapists, music performers, philosophers of music, audiologists, and acousticians.

Finite Versus Infinite

Finite Versus Infinite

Author: Cristian S. Calude

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 376

ISBN-13: 1447107519

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The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g. , does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g. , what is the role played by randomness?, are computers capable of handling the infinity through unconventional media of computation?, how can one approximate efficiently the finite by the infinite and, conversely, the infinite by finite?). Distinguished authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to the volume. Papers are as varied as Professor Marcus' activity, to whom this volume is dedicated. They range from real analysis to DNA com puting, from linguistics to logic, from combinatorics on words to symbolic dynamics, from automata theory to geography, and so on, plus an incursion into the old history of conceptions about infinity and a list of philosophical "open problems". They are mainly mathematical and theoretical computer science texts, but not all of them are purely mathematical.


Book Synopsis Finite Versus Infinite by : Cristian S. Calude

Download or read book Finite Versus Infinite written by Cristian S. Calude and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g. , does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g. , what is the role played by randomness?, are computers capable of handling the infinity through unconventional media of computation?, how can one approximate efficiently the finite by the infinite and, conversely, the infinite by finite?). Distinguished authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to the volume. Papers are as varied as Professor Marcus' activity, to whom this volume is dedicated. They range from real analysis to DNA com puting, from linguistics to logic, from combinatorics on words to symbolic dynamics, from automata theory to geography, and so on, plus an incursion into the old history of conceptions about infinity and a list of philosophical "open problems". They are mainly mathematical and theoretical computer science texts, but not all of them are purely mathematical.

Synthetic Philosophy of Contemporary Mathematics

Synthetic Philosophy of Contemporary Mathematics

Author: Fernando Zalamea

Publisher: National Geographic Books

Published: 2012-09-01

Total Pages: 0

ISBN-13: 0956775012

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A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.


Book Synopsis Synthetic Philosophy of Contemporary Mathematics by : Fernando Zalamea

Download or read book Synthetic Philosophy of Contemporary Mathematics written by Fernando Zalamea and published by National Geographic Books. This book was released on 2012-09-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.

Mathematics and the Body

Mathematics and the Body

Author: Elizabeth de Freitas

Publisher: Cambridge University Press

Published: 2014-06-02

Total Pages: 287

ISBN-13: 1107039487

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This book expands the landscape of research in mathematics education by analyzing how the body influences mathematical thinking.


Book Synopsis Mathematics and the Body by : Elizabeth de Freitas

Download or read book Mathematics and the Body written by Elizabeth de Freitas and published by Cambridge University Press. This book was released on 2014-06-02 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book expands the landscape of research in mathematics education by analyzing how the body influences mathematical thinking.

The Topos of Music

The Topos of Music

Author: Guerino Mazzola

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 1310

ISBN-13: 303488141X

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With contributions by numerous experts


Book Synopsis The Topos of Music by : Guerino Mazzola

Download or read book The Topos of Music written by Guerino Mazzola and published by Birkhäuser. This book was released on 2012-12-06 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by numerous experts

Design Theory

Design Theory

Author: Pascal Le Masson

Publisher: Springer

Published: 2017-04-06

Total Pages: 390

ISBN-13: 3319502778

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This textbook presents the core of recent advances in design theory and its implications for design methods and design organization. Providing a unified perspective on different design methods and approaches, from the most classic (systematic design) to the most advanced (C-K theory), it offers a unique and integrated presentation of traditional and contemporary theories in the field. Examining the principles of each theory, this guide utilizes numerous real life industrial applications, with clear links to engineering design, industrial design, management, economics, psychology and creativity. Containing a section of exams with detailed answers, it is useful for courses in design theory, engineering design and advanced innovation management. "Students and professors, practitioners and researchers in diverse disciplines, interested in design, will find in this book a rich and vital source for studying fundamental design methods and tools as well as the most advanced design theories that work in practice". Professor Yoram Reich, Tel Aviv University, Editor-in-Chief, Research In Engineering Design. "Twenty years of research in design theory and engineering have shown that training in creative design is indeed possible and offers remarkably operational methods - this book is indispensable for all leaders and practitioners who wish to strengthen theinnovation capacity of their company." Pascal Daloz, Executive Vice President, Dassault Systèmes


Book Synopsis Design Theory by : Pascal Le Masson

Download or read book Design Theory written by Pascal Le Masson and published by Springer. This book was released on 2017-04-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the core of recent advances in design theory and its implications for design methods and design organization. Providing a unified perspective on different design methods and approaches, from the most classic (systematic design) to the most advanced (C-K theory), it offers a unique and integrated presentation of traditional and contemporary theories in the field. Examining the principles of each theory, this guide utilizes numerous real life industrial applications, with clear links to engineering design, industrial design, management, economics, psychology and creativity. Containing a section of exams with detailed answers, it is useful for courses in design theory, engineering design and advanced innovation management. "Students and professors, practitioners and researchers in diverse disciplines, interested in design, will find in this book a rich and vital source for studying fundamental design methods and tools as well as the most advanced design theories that work in practice". Professor Yoram Reich, Tel Aviv University, Editor-in-Chief, Research In Engineering Design. "Twenty years of research in design theory and engineering have shown that training in creative design is indeed possible and offers remarkably operational methods - this book is indispensable for all leaders and practitioners who wish to strengthen theinnovation capacity of their company." Pascal Daloz, Executive Vice President, Dassault Systèmes