Review: Mathematics, Nature, Art

Mathematics, Nature, Art by Maria Mannone
My rating: 3 of 5 stars

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.

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