You are here

Aesthetics of Interdisciplinarity: Art and Mathematics

Kristóf Fenyvesi and Tuuli Lähdesmäki, editors
Publication Date: 
Number of Pages: 
[Reviewed by
Joel Haack
, on

Aesthetics of Interdisciplinarity: Art and Mathematics is a useful collection of essays similar to those that appeared in the proceedings of Bridges conferences. In fact, the book is dedicated to the memory of Reza Sarhangi, one of the guiding spirits of Bridges, who died in 2016. Further, nine of the sixteen essays were based on papers that appeared in the proceedings of various Bridges conferences. The editors’ introduction to the book includes a sketch of the history of the Bridges community, mentioning as well the Arts and Mathematics conferences that Nat Friedman organized and their transition to the conferences of the International Society of the Arts, Mathematics, and Architecture (ISAMA). In full disclosure, I was a participant in several of the early Bridges conferences and an ISAMA conference, though my own scholarship at the time concerned connections between mathematics and music. The focus of this book is on connections between mathematics and the visual arts.

Jay Kappraff’s foreward discusses Design Science and points out concepts that are important to both design and mathematics: “elegance, content, duality, simplicity, symmetry, symmetry breaking, managing of stability and instability, cultural context, figure and ground, and color.” [xi] The introductory essay by Tuuli Lähdesmäki and Kristóf Fenyvesi notes, “The aim of this volume is to contribute to the bridge building efforts between cultural and art studies and the mathematical domain of knowledge by exploring interdisciplinary approaches to the aesthetics of mathematical art.”[15] A summary of the various essays follows in the next seven pages. This would be useful to anyone seeking information on a particular approach or topic.

The book is organized into four parts, as discussed below.

The first part of the book contains four essays offering theoretical and philosophical discussions of art and mathematics. Michael Daniel Cohen’s approach is to note the dichotomy of purposes between art, which tells the human story and presents the human view of the world, and science, which seeks the truths of the world independent of us. An historical discussion of the interaction between art and science follows. Sirkkaliisa Usvamen-Routila’s article discusses architecture through the lens of buildings as they are seen. She explores guiding, diagonal lines that are not explicit in the elevations, allowing us to “see” properties that are merely implied. The title of Axel Gelfert’s essay plays on Wigner’s “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” In it Gelfert seeks to understand in what sense one can speak of a mathematical theorem or proof as beautiful. He then discusses ways in which artists since the Renaissance have been inspired by mathematics. Finally, György Darvas first provides a generalized definition of symmetry — if “in the course of any kind of (not necessarily geometrical) transformation (operation), at least one (not necessarily geometrical) characteristic of the affected (arbitrary and not necessarily geometrical) object remains invariant (unchanged)” [82] — which is certainly in accord with how mathematicians use the term. He then discusses (primarily) geometric symmetries and symmetry groups.

The second part of the book includes essays on mathematical principles of composition. Many mathematicians will find the topics discussed here more familiar. Doris Schattschneider discusses symmetry, tilings, the duality of figure and ground, and (especially two-)color symmetries in the art of Maurits Escher. She also provides a brief discussion of Salmon Spirits, a 2007 print by Dylan Thomas, a Coast Salish artist from British Columbia. Slavik Jablan and Ljiljana Radović provide wonderful examples, with discussion, of the works of the originator of op art, Victor Vasarely. Forty-seven colored illustrations of Vasarely’s work in the Vasarely Museum in Hungary accompany the article. Charalampos Saitis’s essay discusses fractals and provides an introduction to fractal art. Dorothy K. Washburn and Donald W. Crowe’s essay demonstrates the value of an approach via pattern symmetries, as opposed to only motifs (decorative patterns), to analyze questions about cultures. The examples are drawn from pottery (Greek neolithic and Pueblo Southwest) and baskets (native Americans in northern California). This part concludes with Paulus Gerdes’s essay, which focuses on a Mozambican weaver, Arlindo Bendezane, who creates baskets that introduce discontinuities of color or design.

The third part of the book contains essays on geometry-based visual art. Angela Vierling-Claassen describes the impact of mathematical models of surfaces on constructivist and surrealist artists of the twentieth century. Satu Kähkönen points out that ornaments serve to suggest certain cultures. She discusses the importance of ornament in the Arabic tradition of design and architecture and argues that the grid (the underlying pattern of regularly spaced lines) is itself an ornament. Part III concludes with Robert V. Moody’s essay concerning paintings of Alice Bosner, a Swiss artist and sculptor who lived in India. Her work was influenced by the geometric principles she discovered in ancient Indian cave art, employing circles, diameters, and chords in a space division and a time division.

In Part IV of the book, three contemporary artists themselves discuss their use of mathematics and science in their works, which are displayed in the book. István Orosz uses anamorphosis, both perspective (oblique) and entoptric (requiring a cylindrical mirror), in three works that interpret literary passages by Shakespeare, Verne, and Poe. He also provides a brief “how to” discussion. Julian Voss-Andreae was inspired to create sculptures that suggest ideas of quantum mechanics. Antol Kelle has created geometric objects that are sliced, allowing them to be manipulated in an interactive way. This part, and the book itself, concludes with an essay by Tuuli Lähdesmäki that discusses the appropriateness of constructivist and concrete art in monuments honoring two Finnish presidents. She considers the public reception of the monuments and suggests three interpretations for the sculptures — metonymic, metaphoric, and symbolic.

This book should be useful for students and researchers with an interest in the connections between art and mathematics. It could provide the basis for independent studies with such students. Additionally, the book could serve as a catalyst for dialogue between mathematicians, philosophers, and artists.

Joel Haack is Professor of Mathematics at the University of Northern Iowa.

See the table of contents in the publisher's webpage.