Mathematics: Muse, Maker, and Measure of the Arts (11w5070)

Arriving Sunday, December 4 and departing Friday December 9, 2011

Organizers

Ingrid Daubechies (Duke University)
Shannon Hughes (University of Colorado at Boulder)
Robert Moody (University of Victoria)
Daniel Rockmore (Dartmouth College)
Yang Wang (Michigan State University)

Objectives

This workshop intends to bring together researchers whose areas of research pertain to the interplay of mathematics and arts. In doing so we hope to promote the application of mathematics to the study of arts, and to develop some coherent frameworks for moving this area of research further ahead. Given the diversity of the research activities this area spans it is impossible to cover all topics comprehensively. We shall focus our workshop mainly on some selected topics. These selected topics will highlight how mathematical and statistical techniques can be valuable tools for the study of arts.

(1) Stylometry Analysis

The evaluation of a work of art for attribution has historically relied on the techniques of connoisseurship, a process by which a questioned work is subjected to the evaluation by a few experts who are steeped in the work and life of the artist in question. The analyses are usually based on their extensive visual experience and encyclopedic knowledge of the career of the would-be artist, as well as other kinds of art historical data. The advent of high definition digitization for works of art has opened up a whole new venue for stylometry analysis. Powerful mathematical and statistical techniques are now available for the study of art, literature and music in terms of authentication and style analysis, motion capturing and more.

Stylometry analysis of literary style has its origins dating back to the mid 1800s. It is Augustus de Morgan, an English logician who first suggested to his friend in a letter in 1851 that �� questions of authorship might be settled by determining the length of words �if one text does not deal in longer words than another��.� This technique and later more sophisticated ones have been used on stylometric analysis of works attributed to Shakespeare. Today, stylometric analysis of literature is already a field that has truly come into its own. Although stylometric analysis of art has lagged and is undoubtly more challenging, time is ripe for it to take off. More importantly, stylometric analysis of art calls for a more diverse and (perhaps more sophisticated) repertoire of mathematical and statistical techniques. The stylometric study by Taylor et al (1999) of Jackson Pollock is based on the fractal property of Pollock�s drip paintings, which shows that Pollock paintings have rather unique fractal signatures. Another pioneer work on stylometry of art was the analysis of drawings that had been attributed to the great Flemish artist Pieter Bruegel the Elder by Lyu et al (2004). In it the use of multiscale wavelet analysis was proposed as a tool for visual stylometry. Beside the Bruegel paintings the technique was also used to analyze a large altarpiece generally attributed to the workshop of the
Renaissance master Perugino. The results of these experiments provided evidence indicating that the wavelet coefficients could be used as a source of information identifying the artist. More recently, in a comprehensive effort to study stylometry of art, several research teams had been put together to study the paintings of Vincent Van Gogh using high resolution digital scans in the ``Van Gogh Project (VGP)." The research by these teams focused on the brush stroke analysis of these paintings using a variety of techniques such as wavelets, hidden Markov trees, sparse coding. A study by Mao et al (2009) focuses on the use of Empirical Mode Decomposition for stylometry analysis. The results of these studies provide evidence that the mathematical study of stylometry of art is a fertile field. One of the objectives of this workshop is to bring researchers with different areas of expertise together to discuss possible new techniques and applications in stylometry analysis.

(2) Mathematical Techniques for Art Making

The advances in the study of geometry, dynamical systems, information theory, learning theory, and others have led to rapid advances in many areas of art making. And conversely, the pursue of new ideas and trends in art such as tiling, origami, computer graphics and abstract art has contributed greatly to the advances in some areas of mathematics. The visually stunning Mandelbrot set and many other fractal sets come from nonlinear dynamical systems, from which the study of chaos was born. Today fractals have been used not only as a generative tool for making beautiful pictures but also a tool for modeling natural objects and physical phenomena such as rough surfaces in material science. The discovery of Penrose tiles has led to the study of aperiodic orders and the study of quasicrystals, and has inspired the Escheresque artistic aspirations of many mathematicians, artists and students.

An important objective of this workshop is to bring experts in these areas to discuss the latest mathematical techniques for art making. Today generative art is an active and broad area of research and practice. Generative art aims for the creation of artwork using algorithms (both deterministic and random). While Mandelbrot set and fractals represent a typical generative art, the field has gone far beyond it. Sophisticated mathematical and statistical techniques are now available to create a wide array of intricate artworks. The diversity of generative art precludes us from touching on all aspects of it. Much of it should be more suited for a workshop on computer graphics. Instead our workshop shall concentrate on generation of art having very strong underlying mathematical theories, with special focuses on dynamical systems, learning theory, differential equations and information theory. We shall also devote part of this workshop to the use of mathematics for aiding art making. An exciting such area is origami. Using sophisticated geometric visualization techniques extraordinary (and often mind-boggling) origami objects have been created in recent years by Montroll, Lang and many others. Now some of these techniques have also found its application in the study of robotics. Mathematical techniques have also been used to enhance and to restore artwork. The work by Chudnovsky brothers on the digital archiving of medieval draperies and the digital restoration and enhancement of old films are also such examples.


It is important to note that one of the objectives of the workshop is to bring together mathematicians and people in the art communities who are otherwise less likely to interact due to the distances in their respective fields of expertise. The suggested topics in this workshop are all of great interest to the art community. It is our belief that only by regularly interacting with the art community can mathematics find its vitality and become an important and lasting component in the of study of arts. In fact, it is also our hope that such interactions will lead to new ideas and problems in mathematics. The field is relatively young and lacks the coherence of many other research areas in mathematics. However, this only makes an even a stronger argument for such a workshop. Indeed we hope this workshop will be the beginning of a long lasting collaboration between mathematicians and the art community.