Abstract
We illustrate the basic ideas and principles of quantum geometry, by considering mutually complementary quantum realizations of circles. It is fascinating that such a simple geometrical object as circle, provides a rich illustrative playground for an entire array of purely quantum phenomena. On the other hand, the ancient Pythagorean musical scale, naturally leads to a simple quantum circle. We explore different musical scales, their mathematical generalizations and formalizations, and their possible quantum-geometric foundations. In this conceptual framework, we outline a diagramatical-categorical formulation for a quantum theory of symmetry, and further explore interesting musical and geometrical interconnections.
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Notes
- 1.
For an arbitrary action, we can surjectively map \(X\times G\) to R via \((x,g)\mapsto (x,xg)\), but the correspondence will be in addition injective (that is, bijective) iff the action is free.
- 2.
We do prefer the term “partiture” because of its semiotic and etymological contents (related to It. Sp. “partitura”, Fr.“partition”).
- 3.
The same interpretation applies to all equalities derived in this diagrammatic theory.
- 4.
Here the square-bracketed indexes simply refer to the associated copy of the initial algebra within the corresponding higher order collectivity algebra.
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Acknowledgements
I am very indebted to Dr. Gabriel Pareyon, for extending me a warm invitation to participate in this Conference, various interesting and fruitful conversations, and unlimited enthusiasm which contributed to creating a unique scientific, academic and artistic atmosphere in Puerto Vallarta.
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Đurđevich, M. (2017). Music of Quantum Circles. In: Pareyon, G., Pina-Romero, S., Agustín-Aquino, O., Lluis-Puebla, E. (eds) The Musical-Mathematical Mind. Computational Music Science. Springer, Cham. https://doi.org/10.1007/978-3-319-47337-6_11
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DOI: https://doi.org/10.1007/978-3-319-47337-6_11
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