Ahead of the upcoming symposium Calculation and Aesthetics, four speakers talked about their personal motivation for dealing with the relationship of two seemingly distant disciplines: Juan Luis Gastaldi (professor for philosophy and aesthetics, École Supérieure des Beaux Arts Montpellier Agglomération, Montpellier/France), Gerard Caris (visual artist, Maastricht/Netherlands), Robert Tubbs (associate professor, Department of Mathematics, University of Colorado Boulder, Boulder, CO/USA), and Martin Beck (philosopher, Berlin).
Juan Luis Gastaldi:
Mathematics as a Setting for the Determination of Common Problems
Can artists and a theoreticians truly exchange ideas at each other’s level of specificity? Is there a point – no matter how elusive – in which aesthetics wouldn’t be different from logic? Is it possible to grasp a form of sensibility which would be at the same time a form of understanding? As domains of creation of meaning, artistic and theoretical practices can both be regarded as forms of expression, sharing therefore the formal conditions of expression as such. In this sense, mathematics, as the field of practice, reflection, and elaboration of formal signs, could be envisaged not as the official and authoritative scientific language, as it is generally thought to be, but as an open setting for the precise definition of common problems. Such a possibility requires, however, the recognition of an aesthetical dimension as being essential for mathematics as such. Only then, maybe – just maybe – could the dividing line between arts and sciences, which was redrawn not so long ago after all, be meaningfully cut across. »My solitude is gladdened by this elegant hope.«
Pentagonism and the Solid Geometry behind Things
Driven by curiosity, I worked myself through a variety of highly specialized jobs as a mechanical engineer, petroleum engineer, draftsman, designer of opto-metrical instruments, and as site engineer for the construction and erection of the Telstar Horn Antenna, through which I became involved in the discoveries of the space race in the United States in 1961. Through these explorations within and through these jobs, a two fold view of reality became apparent: one through a direct view with the naked eye and one through the microscope and calculation. The first view, which only reveals the outward appearance of these installations, does not tell much about the intrinsic nature thereof. The second view, in which the underlying form becomes visible not only to the innocent eye but also – and foremost – to the inner calculating mind’s eye, with which the hidden aspects of the deep fabric of reality becomes comprehensible, is of the greatest importance. Through this, we also developed an aesthetic awestruck appreciation, with which the beautiful intricate organization of the nature of things involving the organic as well as the anorganic nature can be deduced: namely that behind all these things lies a solid geometry. The grid and its three dimensional version, known as a lattice, is considered as the principle structuring element of reality as well as a leading principle in my personal exploration of art in which an entirely new form of development, self-coined as »Pentagonism,« has come into existence. This reveals creations never envisioned before in art, in which an interlinking of art and mathematics becomes self-evident for me and everyone else to see, as well as bringing about an aesthetical appreciation dependent on the prior package of conditioned aspects of the individual.
Mathematic Ideas Influence Artists while They Interpret those Ideas
Why is a mathematician looking at twentieth century art? I am broadly interested in the role of mathematical ideas in non-scientific intellectual or artistic thought. Before I focused on twentieth century literature and art, I published a book, What is a Number? (2009), that examined historical examples to discover that mathematical ideas are not esoteric ones, divorced from other intellectual or artistic pursuits, but are dynamic ones intrinsic to almost every human endeavor. While this has been true at least since the sixth century BCE, in the twentieth century appeals to mathematical ideas outside of science became widespread. In Mathematics in 20th-Century Literature and Art (2014), I focused exclusively on ideas of mathematics in the twentieth century. These examinations ranged from artists who employed mathematical concepts to express their highly non-mathematical aesthetic ideas to artists who used mathematical ideas to structure their art to artists who employed mathematical images in their work. A theme that appears throughout the book is how some artists, writers, and analysts used a loosely axiomatic approach to either develop or explain their work. Why is it important for a mathematician to look at these developments? In the later part of the twentieth century, several mathematicians were highly critical of imprecise appeals to mathematical concepts by literary theorists and philosophers. What mathematicians need to understand is that an artist or theoretician should be expected to modify a mathematical notion while importing it into their work. Indeed that modification is part of the creative process. Our role is not to critique artists’ mathematical precision but to try to understand – and appreciate – their incorporation of mathematical ideas into their works and aesthetics.
Understanding Art’s Relationship to Mathematics is Key to Understand Artistic Thinking
Thinking about the relationship of art and mathematics is crucial for understanding the status and essence of the concept we discuss – since about 10 years as prominently as often elusively – as »artistic thinking,« »artistic research,« or »the knowledge of the arts.« This discussion is only the most recent instance of the question about the relationship of the aesthetic and the rational, which – since the discipline of aesthetics emancipated itself from logic in the eighteenth century – has never been just a straightforward opposition, but a dialectic one. Since Blaise Pascal distinguished »esprit de géometrie« and »esprit de finesse« as two – almost mutually exclusive – approaches to the world, the difference has often be noted. In reverse, no other than Theodor W. Adorno has described how art in modernity increasingly incorporates rational »construction« into its modes of production. The model for this rationality is not philosophic argumentation or empirical research, but mathematics: instead of making propositional assertions about the world, it is based on the immanent organization of elements according to rules. The notion of »artistic thinking« always contains a paradox, as Jacques Rancières formulation of a »thought which does not think« exemplifies. Yet a paradox is never in itself an answer, it rather begs an answer. Mathematics and its technical applications are the most dominant form of rationality in our present society. To understand the status and possibilities of »artistic thinking« today, we have to dig into its relationship to mathematics.