Mathematics, Nature, Art

by Maria Mannone

This book can be read as a journey through music and some forms from nature, in light of mathematics. This is also a journey through unique places in Palermo (Italy), and precisely: the Botanical Garden (the largest in Europe), the Doderlein Museum of Zoology, and the Geology and Paleontology Museum Gemmellaro. Around the end of Eighteenth Century, Palermo was renown worldwide for the Circolo Matematico and its official journal, Rendiconti del Circolo Matematico di Palermo, where Poincar´e, Hilbert, Landau, and Borel published research papers. Taking into account the language of mathematics, and in particular of the most abstract area of mathematics, that is, categories with their diagrams, this book explores some natural shapes displayed in the mentioned places in Palermo, showing how they can be mapped into sound. The book ends with two orchestral pieces, “A Fight for Light” and “Perfect Shapes in the Prehistoric Sea,” based on the proposed ideas. We are trying to build a unitary vision of music, visual arts, and nature. In fact, one of the main characteristics of categories is the possibility of giving a unifying language. At some points of the book, we will be using specific results of category theory.

133 pages, Paperback

Published October 1, 2019

About the author

Maria Mannone is a theoretical physicist and a composer. She achieved her Ph.D. in the US, at the University of Minnesota. She is currently collaborating with the Department of Mathematics and Informatics of the University of Palermo.
She is developing interdisciplinary research between mathematics, music, and the visual arts.

Reviews

[Tom Schulte · Rating 3 out of 5]

This is q quick read, profuse with illustrations exploring the concept of transformation not occulted by rigorous mathematical arguments. From the "Conclusions":


In these pages, we proposed a very short journey through nature, art, and mathematics...

This is not a book about mathematics, nor a book about music, or about biology or geology. This is a book wishing to give some answers to our need to connect things and to find ‘the path’ within complexity.


As such, it recollects to me the narrower in scope also quite lovely (and referred to herein) On Growth and Form by D'Arcy Wentworth Thompson. Like that author, the impetus is an appreciation of beauty and form and linking together abstractions of different, moving expressions:

If science and mathematical concepts can influence aesthetics and artistic production, also the opposite is true: aesthetics can influence scientific research. Aesthetics, elegance of the formalism, and focus on geometry were relevant for the research of the physicist Paul Dirac...

Theorem 4.2.1.
Abstract ideas do not belong to nature, thus we can consider them as colimits or limits using universal properties for natural entities.

While transmutation between forms of development (juvenile to adult, etc.) are common here, the recurring theme is "sonification": creating music constructed from essential elements of a form:

This may give hints about the meaning of images’ sonifications. In fact, sonifying a shape also means to establish a mapping between a sequence of points ‘without time,’ taken from the given shape, to a sequence of events in time (sounds, musical notes performed one after the other). Even if we consider continuous shapes to be mapped into continuous sound sequences, such as a violin glissando, we have to assign a starting time, and an ending time, and thus a duration to the overall process.

I believe artists and artistically minded mathematicians especially those inclined toward nontraditional composition techniques will find the book engaging and potentially enlightening.