A project by UNESCO-MOST – C.I.P.S.H – Mémoire de l’Avenir
“ParadigmaS, The Music of Mathematics” is a multimedia concert, supported by a video-projection that includes animations and explanations, and uses music as a common thread of the evolution of our society. This concert addresses one of the most important subjects of knowledge: the origin of mathematical abstraction and its inherent relation to art, particularly music, sculpture, architecture and painting. A paradigm comprising until the end of the Renaissance, that explains the way in which man conceives and perceives reality, the cosmos, and existence itself.
This spectacle, conceived and created by the lute player and musicologist Samir Suez, presents four musicians from recognized artistic routes and diverse cultural backgrounds (France, Chile, Middle East and Italy). In musical and visual languages, they explain the mathematical relations contained in music and art, which are the basis of the artistic thinking process. The musical repertoire used is that of the sixteenth and early seventeenth century, which best represents the culmination of this paradigm.
The images projected during the musical execution illustrate the way in which these relations function. It expresses, in a poetic and didactic manner, how the classical mathematical model present in music (Pythagorean system), the knowledge of the cosmos (Ptolemaic and Copernic system) and the geometrics’ Golden section or sectio aurea (Euclid, Fibonacci, Da Vinci and even Dali, Le Corbusier, etc.) have been used by Man to understand and represent reality, Cosmos and Nature. In this sense, music is an excellent medium, because, from the point of view of mathematical abstraction, it corresponds to a common form of construction: the same way as classical painting, sculpture and architecture.
Indeed, this ancient paradigm of human knowledge contains varied models of abstract thinking, known in antiquity as quadrivium arts: music, the sound model conceived by Pythagoras in Pan-Hellenic Greece; classical astronomy, which reach the Renaissance through the writings of Ptolemy; Rhetoric or logical form of thought, which enables us to reach the truth; and Geometry for architecture and the golden ratio, present in different forms of Nature. These arts of knowledge construct the forms of human thought from antiquity to the Renaissance, when the classical paradigm collapses and the theory of sciences begin to develop.
The last expression of these models is manifested in the arts during the Renaissance. Personalities such as Leonardo da Vinci, Giordano Bruno, Fibonacci, Niccolò Machiavelli, Nicolaus Copernicus, Johannes Kepler, and Galileo Galilei, among others, emerge as the precursors of our modern thought. A new paradigm is born: an anthropocentric philosophical conception; a Universe centred around the Sun, rather than a static Earth; new continents and revised mathematical models re-proposing the golden section; paradoxes of knowledge giving rise to the transcendental number π, the quadrature of the circle, Fibonacci’s sequence, and the social archetypes corresponding to a society whose aesthetic conception is a reflection of the cosmos and nature. During that period, the golden rectangle, the divine spiral and the pentagram star – geometric forms always present in Nature – are once again recognizable in architecture, painting, sculpture, and music. This is why there is nothing better than the music of the Renaissance to tell the story of the classical paradigm of abstract thinking.
ParadigmaS is a project conceived and designed as an educational resource. It is an artistic spectacle composed by tree different concerts, but its pedagogical character reaches further, illustrating a practical application of mathematics and arts to other aspects of life. This allows the public to approach the ancient modes of understanding, of which art has been always a carrier: a true instrument of conscience that contributes to integrate the different fields of knowledge, offering tools for a global point of view of the evolutionary process of humankind.
We are convinced that Art contributes to Man’s consciousness and conscience is at the very foundation of our human evolution.