Mind matters in mathematics and music
Abstract
Mathematics and music in practice and performance, and in learning and teaching, share many characteristics, such as beauty and harmony, memory and intuition (as internal senses) and mind or intellect. These raise the principles of processing information in mathematics and music and, by implication, the role of an acquaintance with the essentials of perception, abstraction and affective connaturality in teacher education. This paper compares mathematics and music and considers the acquisition of knowledge and skills through the external and internal senses and emotions, utilizing the role of knowledge through multiple intelligences. In doing so it does not canvas the utilities of mathematics and music as fields of human endeavour so much as their role in the cultivation of serenity and knowledge in the cultured mind. This is a theoretical paper but it is based on nearly a century of teaching from the combined work of the two authors in the teaching of music and mathematics. The paper highlights the importance of inspiration in teaching, inspiration built on a thorough basis of the foundations of anthropology to include the emotions as well as the intellect. While teacher education programs rightly concern themselves with knowledge of the field of study, knowledge of pedagogy, they do not always consider the ability to inspire which is at the heart of managing and mentoring people.
Keywords
Full Text:
PDFReferences
Allen, A.L. and A.G. Shannon. (1971). “Concept selection strategies of New Guinea students.” Journal of Experimental Education. 3 (3), 1–4.
Aquino, Frederick D. (2018). “Epistemology.” In Frederick D. Aquino and Benjamin J. King (eds). The Oxford Handbook of John Henry Newman. Oxford: Oxford University Press, Ch.19.
Armstrong, Thomas. (1993). Seven Kinds of Smart. New York: Plume/Penguin.
Block-Schwenk, Kevin. (2020). “Applied Mathematics for Musicians”. Berklee College Prospectus. Boston, MA: Berklee College of Music.
Bloom, Benjamin S. (ed.) (1956). Taxonomies of Educational Objectives. Handbook I: Cognitive Domain. New York: Longmans Green.
Budziszewski, J. (2004). “The natural, the connatural, and the unnatural.” St Thomas and the Natural Law Conference, Jacques Maritain Center, University of Notre Dame, South Bend, Indiana, July.
Connell, W.F. (ed.) (1965). The Foundations of Education. Sydney: Novak.
Dave, R.H. (1970). “Psychomotor levels.” In R. J. Armstrong (Ed.), Developing and writing behavioral objectives. Tucson: Educational Innovators Press.
Ehert, Matthew. (2020). “The plasma universe and Max Planck’s musical spacetime rediscovered.” Nexus. June-July, pp.57-62.
Freni, Cristine. (2016). Homo aestheticus: la bellezza come cura per l’antropologia del nostro tempo. Studia Moralia. 54(2), 251-272.
Frey, Angelica. (2015). “Can we write music as functions? Yes.” CMUSE. July 15.
Gardner, H. (1983). Frames of mind - the theory of multiple intelligences, New York, NY: Basic Books.
Gardner, Howard. (2011). Truth, beauty, and goodness reframed: Educating for the virtues in the 21st century. New York: Basic Books.
Griffin, Michael. (2013). Learning Strategies for Musical Success. Adelaide, SA: Music Education World, Ch.4.
Hardy, G.H. (1967). A Mathematician's Apology. With a foreword by C.P. Snow. Cambridge: Cambridge University Press. (1st published 1940).
Harrison, Clive. (2017). “The songwriting coalface: where multiple intelligences collide.” Australian Institute of Music Occasional Papers, No.47.
Iverson, K.E. (1980). “Notation as a Tool of Thought.” Communications of the Association for Computing Machinery. 23(8), 444-465.
Jaroszynski, Piotr. (2011).” Aquinas metaphysics: versus mythology, ontology, and ideology.” Thomism and Asian Cultures: Celebrating 400 Years of Dialogue Across Civilizations, Quadricentennial International Philosophy Conference, University of Santo Thomas, Manila, Philippines.
Krathwohl, D.R., B.S. Bloom and B.B. Masia. (1964). Taxonomy of Educational Objectives. Handbook II: Affective Domain. New York: David McKay.
Levitin, Daniel. (2019). This is Your Brain on Music: Understanding a Human Obsession. London: Penguin Life.
Levitin, Daniel. (2020). Successful Aging: A Neuroscientist Explores the Power and Potential of Our Lives. London: Penguin Life.
Leyendekkers, J.V. and A.G. Shannon. (2013). “On the Golden Ratio.” Advanced Studies in Contemporary Mathematics. 23(1), 195-201.
Lisska, Anthony J. (2016). Aquinas's Theory of Perception: An Analytic Reconstruction. Oxford: Oxford University Press.
Lombo, José Angel and Francesco Russo. (2007). Philosophical Anthro-pology: An Introduction. Downers Grove, IL: Midwest Theological Forum, Chs.6,7.
Manly, B.F.J. and A.G. Shannon. (1974). “An analogical replication of a Piagetian experiment on New Guineans.” Malaysian Journal of Education. 11(1), 77–82.
Maor, Eli. (2018). Music by the Numbers: From Pythagoras to Schoenberg. Princeton, NJ: Princeton University Press.
Maritain, Jacques. (1953). The Range of Reason. London: Geoffrey Bless.
Maritain, Jacques. (1969). “Quelques réflexions sur le savoir théologiques.” Revue Thomiste. 69: 3-27.
Miller, B.R.J. sm. (1961). The Range of Intellect. London: Geoffrey Chapman.
Nagy, Mariana, Simon R. Covell and Valeriu Beiu. (2018). “Are 3D Fibonacci spirals for real?: From Science to Arts and Back to Science.” Proceedings of the 7th International Conference on Computers Communication and Control. Oradea, Romania: IEEE, pp.91-96.
Neuhaus, Heinrich. (2016). The Art of Piano Playing. (Translated and edited by K.A. Leibovitch.] London: Kahn and Averill.
Newman, J.H. (1985). An Essay in Aid of a Grammar of Assent. (Edited by I.T. Ker). Oxford: Clarendon Press.
Ngô-Tiêng-Hiên. (1971). “Art et vêritiê dans l’oeuvre d’Etienne Souriau.” Revue Philosophique de Louvain. 69(1), 73-91.
Pascual-Leone, Juan. (1970). “A Mathematical Model for the Transition Rule in Piaget’s Development Stages.” Acta Psychologica. 32(4), 301-345.
Phillips, George M. (2005). Mathematics is Not a Spectator Sport. New York: Springer.
Sanchez Martinez, Jorge Julian. 2020. “A mathematical assessment on the ontology of time.” Science and Philosophy. 8 (2): 91-104.
Sautoy, Marcus du. (2011). “Listen by numbers: music and maths.” The Guardian. June 28.
Schonberg, Harold C. (1987). The Great Pianists from Mozart to the Pre-sent, 2nd edition. New York: Simon and Schuster.
Seibert, Scott E., Marie L. Kramer and Peter A. Heslin. (2016). “Developing career resilience and adaptability.” Organizational Dynamics. 45(3): 245-257.
Shannon, A.G. (1969). “Jacques Maritain and the philosophical foundations of education.” Education Today: Journal of the College of Preceptors. 19(3), 20.
Shannon, A.G. (1991). “Shrewd guessing in problem-solving.” International Journal of Mathematical Education in Science and Technology. 22(1), 144–147.
Shannon, A.G. (2008). “An Interpretation of Pascual-Leone’s Discrete Mathematical Model of Human Information Processing Capacity.” Notes on Number Theory and Discrete Mathematics. 14 (2): 15-20.
Shannon A.G. (1982). “Note on an Algebraic Structure for a Concept Space.” Journal of Structural Learning. 7(2): 143-149
.
Shannon, Anthony G., Irina Klamka and Robert van Gend. (2018). “Generalized Fibonacci Numbers and Music.” Journal of Advances in Mathematics. 14(1), 7564-7579.
Siepmann, Jeremy. (2010). “The Art of Doing.” International Piano Magazine, September/October, Symposium.
Smith, Vincent Edward. (1960). The School Examined: Its Aim and Content. Milwaukee, WI: Bruce.
Stakhov, Alexy. (2020). Mathematics of Harmony as a New Interdisciplinary Direction and “Golden” Paradigm of Modern Science. Singapore: World Scientific.
Sullivan, J.W.N. (1926). Aspects of Science: Second Series. New York: Alfred A Knopf, pp.93-94.
Taruskin, Richard. (2005). The Oxford History of Western Music: Volume I – The Earliest Notations to the Sixteenth Century. Oxford: Oxford University Press.
Unger, Roberto Mangabeira and Lee Smolin. (2014). The Singular Universe and the Reality of Time. Cambridge: Cambridge University Press.
Wildridge, Justin. (2019). “Classical Music and Mathematics.” CMUSE. May 4.
Zattorre, Robert J., Joyce L. Chen and Virginia B. Penhune. (2007). “When the brain plays music: auditory-motor interactions in music percep-tion and production.” Nature Neuroscience. 8: 57-558.
DOI: http://dx.doi.org/10.23756/sp.v9i1.593
Refbacks
- There are currently no refbacks.
Copyright (c) 2021 Anthony (Tony) Greville Shannon
This work is licensed under a Creative Commons Attribution 4.0 International License.
Science & Philosophy - Journal of Epistemology, Science and Philosophy. ISSN 2282-7757; eISSN 2282-7765.