EAN: 9783030851897

COMPUTATIONAL MUSIC SCIENCE FUNCTORIAL SEMIOT...

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 Cech 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.

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