By Michele Emmer
Mathematics and Culture
I started my annual conference on Mathematics and Culture in Venezia at the university of Ca’ Foscari in 1997. In this meeting the relationships between art and mathematics are of great importance. Many artists and mathematicians have participated and have written texts for the proceedings published first in Italian then in English. At the most recent meeting I made an overview of all the projects I have been involved in recent years connecting mathematics and culture, mathematics and art in particular. So I gave a presentation of the Visual Mind project.
In 1977 Frank J. Malina, a founding member of Leonardo, the journal on the relationships between art, science and technology wrote the following in the preface of the volume Visual Art, Mathematics & Computers:
In one way or another, mathematics underlies the ideas and the artworks discussed – only elementary echoes are evident in some, but there are sophisticated applications of the ‘queen of sciences’ in others. To understand the non-figurative or abstracts artworks presented requires, in general, a comprehension of messages of a kind different from those that artists have traditionally used – works generally needs an understanding of messages that are of a different nature from those traditionally used by artists.
Will these new developments take to a synthesis between art and mathematics? Digital computers offer many possibilities for two- and three-dimensional art, both figurative and non-figurative. Some artists have engaged computers as an aid to creativity. The volume is to understand whether artists will have a more serious interest in cybernetic aesthetics than that they had in past theories on aesthetics, thus arriving at a synthesis between mathematics and art. These words, written in 1977, inspired the project The Visual Mind, on the relationship between mathematics and art.
Since then, many years have gone by and computers have profoundly modified the way of life of at least a part of humanity. Among other possibilities, computers are instruments that allow developing mathematical experiments that open entirely new perspectives. The scanty graphic capacities computers were equipped with at the end of the sixties have become ever more sophisticated, leading to the development of another important chapter in the relationship between mathematics and art.
It became possible to construct a surface on a video terminal and to move it and transform it in order to study its properties. In addition to being aids to intuition, computers became essential instruments for the construction of models. The great potential of computer graphics as a research tool was recognised by mathematicians as soon as the new technologies were available. As tools and software became more sophisticated, the depth and the relevance of the applications of computer graphics to mathematical problems increased. After the first steps in the seventies, the significant increase of computer graphics in mathematics has lead to the development of a specific area of mathematics that can be called Visual Mathematic. It is not only – as could be imagined – rendering visual or visualising well-known phenomena through graphic tools, but rather, using visual instruments to make oneself an idea of mathematical problems that are still open. Thus, it refers to the use of the computer as a tool to experiment and formulate conjectures in and of itself.
The Visual Mind
We are probably at the beginnings of an ever larger dissemination of images created by mathematicians. The availability of computers with improved graphic capacity is opening a new area of research for mathematicians, which could make computer graphics, become, in a not too distant future, a unifying language between art and science. We cannot do otherwise than be joyful about this widespread collaboration between mathematicians and artists. Even if a new Renaissance is not highly probable, interesting results can be expected.
Just as mathematics provides us with a primary method of cognition, some of its basic elemenbts will furnish us with laws to appraise the interactions of separate objects , one to another. Since it is mathematics which lebnds siginficance to these relationships it is only a natural step from having perceived them to desiring to portray them. . . . They undoubtedly provoke an aesthetic reaction in the beholder”, wrote Max Bill in 1949. Can these thoughts also be applied to the images that mathematicians have created in the last years? Without wanting to privilege computer graphics as an exclusive means of artistic expression. It is just another tool, another instrument at the disposition of mathematicians and artist.
Addressing these topics and more, such as the relationship that has taken place throughout time between mathematics, art, architecture, as well as cinema, was the aim of the project The Visual Mind. Given the widespread interest of the first volume, in 1999 I started working on a new and updated volume. With the cooperation of artists, mathematicians, art historians, architects, and filmmakers, The Visual Mind II was published last June.