Quantum GestART: identifying and applying correlations between mathematics, art, and perceptual organization

Journal of Mathematics and Music

Volumn 15, Issue 1, 2021, Pages 62-94

  Mannone, Maria ^a   Favali, Federico ^b   Di Donato, Balandino ^c   Turchet, Luca ^d  

^a UNIVERSITY OF PALERMO   (Italy)

^b UNIVERSIDAD NACIONAL DE TRES DE FEBRERO   (Argentina)

^c UNIVERSITY OF LEICESTER   (United Kingdom)

^d UNIVERSITY OF TRENTO   (Italy)

Author keywords

diagrams; Dirac notation; Gestalt; Gestural similarity; sonification

Indexed keywords

EID: 85081587457     PISSN: 17459737     EISSN: 17459745     Source Type: Journal    
DOI: 10.1080/17459737.2020.1726691     Document Type: Article

References (87)

1. Abadi, Martín, Paul, Barham, Jianmin, Chen, Zhifeng, Chen, Andy, Davis, Jeffrey, Dean, Matthieu, Devin, et al. 2016. “TensorFlow: A System for Large-Scale Machine Learning.” In Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI '16), 265–283. https://www.usenix.org/system/files/conference/osdi16/osdi16-abadi.pdf.
2. Allen, Paul G., and Paul A., Kolers. 1981. “ Sensory Specificity of Apparent Motion.” Journal of Experimental Psychology: Human Perception and Performance 7 (6): 1318–1326.
3. Alunni, Charles., 2004. “Diagrammes et catégories comme prolégomènes à la question: qu'est-ce que s'orienter diagrammatiquement dans la pensée ?” In Penser par le diagramme–de Gilles Deleuze à Gilles Châtelet, edited by Batt Nöelle. Paris: Presse Universitaire de Vincennes.
4. Alunni, Charles., 2013. “De La Traducibilité Des Savoirs.” Review Sciences/Lettres 1, 1–14. http://rsl.revues.org/293.
5. Aphex Twin, 1999. “Windowlicker.” CD. Warp Records–WAP105CD.
6. Amiot, Emmanuel., 2016. Music Through Fourier Spaces: Discrete Fourier Transform in Music Theory. Heidelberg: Springer.
7. Arias, Juan Sebastián., 2018. “Spaces of Gestures are Function Spaces.” Journal of Mathematics and Music 12 (2): 89–105.
8. Baez, John, and Lauda, Aaron. 2011. “A Prehistory of n-Categorical Physics.” In Deep Beauty: Understanding the Quantum World Through Mathematical Innovation, edited by Hans Halvorson, 13–128. Cambridge: Cambridge University Press.
9. Campbell, Edward., 2013. Music after Deleuze. London: Bloomsbury.
10. Caramello, Olivia., 2016. “The Theory of Topos-Theoretic ‘Bridges’–A Conceptual Introduction.” Glass-Bead. Accessed 9 November 2018. https://www.glass-bead.org/article/the-theory-of-topos-theoretic-bridges-a-conceptual-introduction/?lang=enview
11. Caramello, Olivia., 2018. Theories, Sites, Toposes. New York, NY: Oxford University Press.
12. Coecke, Bob., 2006. “Introducing Categories for the Practising Physicist.” In What is Category Theory? Advanced Studies in Mathematics and Logic. Vol. 30, edited by Giandomenico Sica, 45–74. Monza: Polimetrica Publishing.
13. Cohen-Tannoudji, Claude, Bernard, Diu, and Franck, Laloë. 2005. Quantum Mechanics. Paris: Wiley-VCH.
14. Collins, Tom, Maria, Mannone, Delilah, Hsu, and Dimitri, Papageorgiou. 2018. “Psychological Validation of the Mathematical Theory of Musical Gestures.” Submitted.
15. Culbertson, Jared, and Kirk, Sturtz. 2013. “Bayesian Machine Learning via Category Theory.” ArXiV. https://arxiv.org/abs/1312.1445.
16. Dalla Chiara, Maria L., Roberto, Giuntini, Roberto, Leporini, Eleonora, Negri, and Giuseppe, Sergioli. 2015. “Quantum Information, Cognition, and Music.” Frontiers in Psychology 6, 1583.
17. D'Arcy Thompson, Wentworth., 1966. On Growth and Form, an Abridged Edition, edited by John Tyler Bonner. Cambridge: Cambridge University Press.
18. Deleuze, Gilles., 1986. Foucault. Paris: Les Éditions de Minuit.
19. Deroy, Ophelia, Anne-Sylvie, Crisinel, and Charles, Spence. 2013. “ Crossmodal Correspondences Between Odors and Contingent Features: Odors, Musical Notes, and Geometrical Shapes.” Psychonomic Bulletin and Review 20, 878–896.
20. Deroy, Ophelia, and Charles, Spence. 2013. “ Why We Are Not All Synesthete (Not Even Weakly So).” Psychonomic Bulletin and Review 20 (4): 643–664.
21. Dirac, Paul A. M., 1939. “ A New Notation for Quantum Mechanics.” Mathematical Proceedings of the Cambridge Philosophical Society 35, 416–418. http://journals.cambridge.org/abstract_S0305004100021162.
22. Ehresmann, Andrée C., and Jaime, Gomez-Ramirez. 2016. “ Conciliating Neuroscience and Phenomenology Via Category Theory.” Progress in Biophysics and Molecular Biology (JPMB) 19 (2): 347–359.
23. Ehresmann, Andrée C., and Jean-Paul, Vanbremeersch. 2007. Memory Evolutive Systems. Amsterdam: Elsevier.
24. Fiore, Thomas, and Thomas, Noll. 2011. “Commuting Groups and the Topos of Triads.” Proceedings of the 3rd International Conference on Mathematics and Computation in Music, edited by Carlos Agon, Emmanuel Amiot, Moreno Andreatta, Gérard Assayag, Jean Bresson, John Manderau, 69–83. Heidelberg: Springer.
25. Fong, Brendan, David, Spivak, and Rémy, Tuyéras. 2019. “Backpropagators as Functor: A Compositional Perspective on Supervised Learning.” ArXiV. https://arxiv.org/pdf/1711.10455.pdf.
26. Gabor, Dennis., 1947. “Acoustical Quanta and The Theory of Hearing.” Nature 159 (4044): 591–594.
27. beim Graben, Peter, and Reinhard, Blutner. 2017. “Toward a Gauge Theory of Musical Forces.” In Proceedings of the 10th International Conference on Quantum Interaction (QI 2016), ed. Jose Acacio de Barros, Bob Coecke, and Emmanuel Pothos, 99–111. Cham: Springer International Publishing.
28. beim Graben, Peter, and Reinhard, Blutner. 2019. “ Quantum Approaches to Music Cognition.” Journal of Mathematical Psychology 91, 38–50.
29. Hallé, Francis, Roleof A. A., Olderman, and Philip Barry, Tomlinson. 1978. Tropical Trees and Forests: An Architectural Analysis. Berlin: Springer-Verlag.
30. Heinrich, Greg., 2014. “Image Segmentation Using DIGITS 5”, NVDIA Developer Blog, November. https://devblogs.nvidia.com/image-segmentation-using-digits-5/
31. Hermann, Thomas, Andy, Hunt, and John, Neuhoff. 2011. The Sonification Handbook. Berlin: Logos Verlag Berlin.
32. Hillier, Jean, and Gareth, Abrahams. 2013. Deleuze and Guattari: Jean Hillier in Conversation with Gareth Abrahams. The University of Liverpool Repository. Association of European Schools of Planning, Wroclaw, Poland. https://livrepository.liverpool.ac.uk/3004625/1/aesop-ya-booklet-series-a-vol-1-deluze-and-guattari-jean-hillier-in-conversation-with-gareth-abrahams.pdf.
33. Jedrzejewski, Franck., 2006. Mathematical Theory of Music. Paris: Delatour France–IRCAM.
34. Jedrzejewski, Franck., 2019. Hétérotopies musicales. Modèles mathématiques de la musique. Paris: Hermann.
35. Kainen, Paul C., 2009. “ On the Ehresmann-Vanbremeersch Theory and Mathematical Biology.” Axiomathes 19, 225–244.
36. Kelkar, Tejaswinee, and Alexander Refsum, Jensenius. 2017. “Analyzing Free-Hand Sound-Tracings of Melodic Phrases.” Applied Sciences 8 (135): 1–21.
37. Khrennikov, Andrei., 2010. Ubiquitous Quantum Structure: From Psychology to Finance. Berlin: Springer.
38. Krähenbühl, Philipp, Vladlen, Koltun. 2011. “Efficient Inference in Fully Connected CRFs with Gaussian Edge Potentials.” Advances in Neural Information Processing Systems 24: 109–117.
39. Kubota, Akihiro, Hirokazu, Hori, Makoto, Naruse, and Fuminori, Akiba. 2017. “A New Kind of Aesthetics–The Mathematical Structure of the Aesthetic.” Philosophies 3 (14): 1–10.
40. Kubovy, Michael, and Michael, Schutz. 2010. “ Audio-visual Objects.” Review of Philosophy and Psychology 1 (1): 41–61.
41. Kubovy, Michael, and Minhong, Yu. 2012. “ Multistability, Cross-modal Binding and the Additivity of Conjoint Grouping Principles.” Philosophical Transactions of the Royal Society B 367, 954–964.
42. Kundu, A., V. Vineet and V. Koltun. 2016. “Feature Space Optimization for Semantic Video Segmentation,” 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, pp. 3168–3175.
43. Küssner, Mats, and Baptiste, Caramiaux. 2015. “Motor Invariants in Gestural Responses to Music.” Proceedings of the International Conference on the Multimodal Experience of Music. https://www.hrionline.ac.uk/openbook/chapter/ICMEM2015-Kussner.
44. Lacquaniti, Francesco, Carlo, Terzuolo, and Paolo, Viviani. 1984. “Global Metric Properties and Preparatory Processes in Drawing Movements.” In Preparatory States and Processes, edited by Sylvan Kornblum and Jean Requin, 357–370. Hillsdale: Psychology Press.
45. Lawvere, William, and Stephen, Schanuel. 2009. Conceptual Mathematics. A First Introduction to Categories. Cambridge: Cambridge University Press.
46. Lerdhal, Fred, and Ray, Jackendoff. 1983. A Generative Theory of Tonal Music. Cambridge: MIT Press.
47. Letelier, Juan-Carlos, Jorge, Soto-Andrade, Flavio Guinez, Abarzua, Athel, Cornish-Bowden, and Maria Luz, Cardenas. 2006. “Organizational Invariance and Metabolic Closure: Analysis in Terms of (M,R) Systems.” Journal of Theoretical Biology 238, 949–961.
48. Mac Lane, Saunders., 1978. Categories for the Working Mathematician. Heidelberg: Springer.
49. Mannone, Maria., 2011. Dalla Musica all'Immagine, dall'Immagine alla Musica. Palermo: Compostampa.
50. Mannone, Maria., 2017. “Gestures between Scores and Acoustics: A Creative Application to Orchestra.” PhD dissertation, University of Minnesota, 2018. https://conservancy.umn.edu/handle/11299/188931.
51. Mannone, Maria., 2018a. “ Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra.” Journal of Mathematics and Music 12 (2): 63–87.
52. Mannone, Maria., 2018b. “cARTegory Theory: Framing Aesthetics of Mathematics.” Journal of Humanistic Mathematics 9 (1): 277–294. https://scholarship.claremont.edu/jhm/vol9/iss1/16/.
53. Mannone, Maria., 2018c. “Knots, Music and DNA.” Journal of Creative Music Systems 2 (2): 1–20. https://www.jcms.org.uk/article/id/523/.
54. Mannone, Maria., 2019. Mathematics, Nature, Art. Palermo: Palermo University Press.
55. Mannone, Maria, Tom, Collins, Delilah, Hsu, and Dimitri, Papageorgiou. 2018. “Mathematical Theory of Musical Gestures, Gestural Similarity, and Psychology: A First Validating Experiment.” Poster presentation at WiMIR Workshop, MIR satellite event, Paris, September 2018.
56. Mannone, Maria, and Giuseppe, Compagno. 2014. “Characterization of the Degree of Musical Non-Markovianity.” https://arxiv.org/abs/1306.0229.
57. Mannone, Maria, and Federico, Favali. 2019. “Categories, Musical Instruments, and Drawings: A Unification Dream.” In Proceedings of the Mathematics and Computation in Music Conference 2019, Madrid, edited by Mariana Montiel, Francisco Gómez-Martín, and Octavio A. Agustín-Aquino, 59–72. Heidelberg: Springer.
58. Mannone, Maria, and Luca, Turchet. 2019. “Shall We (Math and) Dance?” In Proceedings of the Mathematics and Computation in Music Conference 2019, Madrid, ed. Mariana Montiel, Francisco Gómez-Martín, and Octavio A. Agustín-Aquino, 84–97. Heidelberg: Springer.
59. Mazzola, Guerino, and Moreno, Andreatta. 2010. “Diagrams, Gestures and Formulae in Music.” Journal of Mathematics and Music 1 (1): 23–46.
60. Mazzola, Guerino., 2018. The Topos of Music, second edition. Heidelberg: Springer.
61. Niinisalo, Jarmo., 2017. “The Aphex Face ” (blogpost). http://www.bastwood.com/?page_id=10.
62. Nobile, Luca., 2013. “Words in the Mirror: Analysing the Sensorimotor Interface between Phonetics and Semantics in Italian.” In Iconicity in Language and Literature 10: Semblance and Signification, edited by Pascal Michelucci, Olga Fischer, and Christina Ljungberg, 101–131. Amsterdam/Philadelphia: John Benjamins.
63. Northoff, Georg, Naotsugu, Tsuchiya, and Hayato, Saigo. 2019. “Mathematics and the Brain–A Category Theoretic Approach to go Beyond the Neural Correlates of Consciousness.” ArXiV. https://www.biorxiv.org/content/10.1101/674242v1.
64. Plamondon, Réjean, and Wacef, Guerfali. 1998. “ The 2/3 Power Law: When and Why? ” Acta Psychologica 100, 85–96.
65. Phillips, Steven, and William, Wilson. 2010. “Categorical Compositionality: A Category Theory Explanation for the Systematicity of Human Cognition.” PLoS Computational Biology 6 (7): 1–14. https://doi.org/10.1371/journal.pcbi.1000858.
66. Popoff, Alexandre, Moreno, Andreatta, and Andrée, Ehresmann. 2015. “A Categorical Generalization of Klumpenhouwer Networks.” In Mathematics and Computation in Music. MCM 2015, edited by Tom Collins and Anja Volk. Heidelberg: Springer.
67. Prusinkiewicz, Przemyslaw, and James, Hanan. 1980. Lindenmayer Systems, Fractals, and Plants. Lecture Notes in Biomathematics. New York: Springer-Verlag.
68. Prusinkiewicz, Przemyslaw, and Aristid, Lindenmayer. 2004. The Algorithmic Beauty of Plants. New York: Springer.
69. Repp, Bruno., 1992. Music as Motion: A Synopsis of Alexander Truslit's (1938) “Gestaltung und Bewegung in der Musik.” Haskins Laboratories Status Report on Speech Research, SR-111/112: 265–278.
70. Reybrouck, Mark., 1997. “Gestalt Concepts and Music: Limitations and Possibilities.” In Proceeding Music, Gestalt, and Computing–Studies in Cognitive and Systematic Musicology, edited by Marc Leman, 57–69. Heidelberg: Springer.
71. Rocchesso, Davide, and Maria, Mannone. 2018. “Embryo of a Quantum Vocal Theory of Sound.” In Conference of Musical Informatics (CIM) Proceedings, Udine. http://cim.lim.di.unimi.it/2018_CIM_XXII_Atti.pdf.
72. Rogińska, Agnieszka, Kent, Friedman, and Hariharan, Mohanraj. 2013. “Exploring Sonification for Augmenting Brain Scan Data.” In Proceedings of the International Conference on Auditory Display. http://hdl.handle.net/1853/51653.
73. Rosen, Robert., 1958. “ The Representation of Biological Systems From the Standpoint of the Theory of Categories.” Bulletin of Mathematical Biophysics 20 (4): 317–341.
74. Rosenblum, Lawrence D., James W., Dias, and Josh, Dorsi. 2016. “ The Supramodal Brain: Implications for Auditory Perception.” Journal of Cognitive Psychology 29 (1): 65–87.
75. Schutz, Michael, and Scott, Lipscomb. 2007. “ Hearing Gestures, Seeing Music: Vision Influences Perceived Tone Duration.” Perception 36 (6): 888–897.
76. Sparavigna, Amelia Carolina, and Roberto, Marazzato. 2016. “Ket Vectors in Three-Dimensional Space and their Cross Product.” HAL Archives-Ouvertes. https://hal.archives-ouvertes.fr/hal-01288341/document.
77. Spence, Charles., 2015. “Crossmodal Perceptual Organization.” In Oxford Handbook of Perceptual Organization, edited by Johan Wagemans. Oxford: Oxford University Press.
78. Spence, Charles and Cesare V. Parise. 2012. “ The Cognitive Neuroscience of Crossmodal Correspondences ” i-Perception 3 (7): 410–412.
79. Sturm, Bob, Oded, Ben-Tal, Úna, Monaghan, Nick, Collins, Dorien, Herremans, Elaine, Chew, Gaëtan, Hadjeres, Emmanuel, Deruty, and Francois, Pachet. 2018. “ Machine Learning Research that Matters for Music Creation: A Case Study.” Journal of New Music Research 48 (1): 1–21. https://www.tandfonline.com/doi/abs/10.1080/09298215.2018.1515233?journalCode=nnmr20.
80. Thoret, Etienne, Mitsuko, Aramaki, Christophe, Bourdin, Lionel, Bringoux, Richard, Kronland-Martinet, and Sølvi, Ystad. 2014. “Audio-Motor Synchronization: The Effect of Mapping Between Kinematics and Acoustic Cues on Geometric Motor Features.” In Sound, Music, and Motion. CMMR 2013, edited by Mitsuko Aramaki, Olivier Derrien, Richard Kronland-Martinet, and Sølvi Ystad. Cham: Springer.
81. Thoret, Etienne, Mitsuko, Aramaki, Lionel, Bringoux, Sølvi, Ystad, and Richard, Kronland-Martinet. 2016. “ Seeing Circles and Drawing Ellipses: When Sound Biases Reproduction of Visual Motion.” PLoS ONE 11 (4): e0154475.
82. Thoret, Etienne, Mitsuko, Aramaki, Richard, Kronland-Martinet, Jean-Luc, Velay, and Sølvi, Ystad. 2014. “From Sound to Shape: Auditory Perception of Drawing Movements.” Journal of Experimental Psychology: Human Perception and Performance 40 (3): 983–994.
83. Weyl, Hermann., 1952. Symmetry (reprint 2016). Princeton, NJ: Princeton Science Library.
84. Wilczek, Franck., 2016. A Beautiful Question: Finding Nature's Deep Design. New York: Penguin Books.
85. Xenakis, Iannis., 2001. Formalized Music: Thought and Mathematics in Composition (revised edition). New York: Pendragon Press.
86. Youssry, Akram, Ahmed, El-Rafei, and Salwa, Elramly. 2015. “ A Quantum Mechanics-Based Framework for Image Processing and Its Application to Image Segmentation.” Quantum Information Processing 14 (10): 3613–3638.
87. Zbikowski, Lawrence., 2017. “Music, Analogy, and Metaphor.” In The Routledge Companion to Music Cognition, edited by Richard Ashley and Renee Timmers, 501–512. New York: Routledge.