International Society for




Society President: Michael Leyton (USA)

Governing Board:  Jan Beran (Germany), Corey Cerovsek (USA), John Clough (USA), Thaddeus Cowan (USA), Roy Eagleson (Canada), Athanassios Economou (USA), Martin Elvis (USA), Roberto Ferretti (France), Paul Fishwick (USA), Nathaniel Friedman (USA), John Gero (Australia), German Golitsyn (Russia), Bill Hammel (USA), Mike Holcombe (UK), Slavik Jablan (Jugoslavia), Oleg Kisljuk (Russia), Reinhard Kopiez (Germany),Vladimir Koptsik (Russia), Ramesh Krishnamurti (USA), Paul Lansky (USA), Frederic Leymarie (USA),  Arthur Loeb (USA), Jeff Long (USA), Christopher Longuet-Higgins (UK), Guerino Mazzola (Switzerland), Denes Nagy (Japan), Thomas Noll (Germany), Jean Petitot (France), Vladimir Petrov (Russia), Roland Posner (Germany), Galina Riznichencko (Russia), Dan Rockmore (USA), Ed Rothstein (USA), Antonino Saggio (Italy), Reza Sarhangi (USA), Daniel Schodek (USA), Charles Schmidt (USA), Barry Smith (USA), Vera W. de Spinadel (Argentina), George Stiny (USA), Alexander Voloshinov (Russia), Dorothy Washburn (USA),Yasunari Watanabe (Japan), Robert Wechsler (Germany), Lebbeus Woods (USA), Robert Zimmer (UK).

The computational analysis of design is now a enormous discipline involving the interaction of high-level mathematics with advanced programming technologies. All design attempts to satisfy two constraints: functionality and aesthetics. Even a discipline as functionally oriented as structural engineering, in fact, involves aesthetic control over systems of non-linear equations. Aesthetics allows for (1) productive unification of perception, reasoning, and action, (2) understandability despite complexity, (3) generalization and re-usability, (4) axiomatic economy and principled prediction. Aesthetics is a major force in each of the following areas:

Computer-Aided Design and Manufacturing, Robot Motion Design: There has been considerable convergence in mathematics across the different types of CAD (e.g., in architecture and mechanical design), as well as manufacturing by shape-sculpting technology, and robot motion design. We note that Frank Gehry's Guggenheim museum at Bilbao was possible because James Glymph imported into architecture a major program designed by the French for aerospace engineering. The reason for the converging unity is that each of the several disciplines involves analysis of spatial systems of movement, control, and shape deformation - whose natural description is Lie algebras, tensor geometry with exterior differential calculus, and algebraic geometry.

Analysis of Artistic Masterpieces.  Remarkable advances have been made in the mathematical and computational analysis of major artistic masterpieces - from the chorales of Bach, the piano sonatas of Beethoven, to the paintings of Picasso and Raphael, etc. Again, these analyses mainly involve Lie groups, Lie algebras, algebraic and differential geometry.

Scientific Theory-Building and Reasoning: It has been well-recognized that aesthetic criteria play a powerful role in determining the design of theoretical models (e.g., irreducible representations of compact Lie algebras predicted the particle systems of quantum mechanics), as well as the dynamic equations of physics (e.g., Paul Dirac declared that the design of his relativistic electron equation was determined primarily by aesthetic criteria). The problem of insight in theory-building, problem-solving, and reasoning generally has been tackled with significant advances in AI - particularly in the problem-reformulation community, which is based strongly on the aesthetic supervision of discrete algebraic systems.

Software Design: It is clear that aesthetic criteria play a major role in determining software cohesion and decomposition, e.g., module decomposition in structured programming, object decomposition in object-oriented technology. Furthermore, it is apparent that there has been a remarkable interaction between the design of software and the software of design - and that this self-referring advance is driven by the need for aesthetic structuring of systems of computational operations.

The International Society for Mathematical and Computational Aesthetics is concerned with any design object, whether it be the machine-sculpted surface of a car body, the Beethoven Hammerklavier sonata, the Feynman propagator in quantum electrodynamics, or re-usable software. We are concerned with advanced research in four directions: (1) how the design decision-flow is controlled by aesthetics; (2) what structural aspects of a design object are taken to be aesthetic; (3) how aesthetic value is computed by the designer and user; and (4) how aesthetics is integrated with function in the design object.

The board members of this society are internationally known for their extensive and highly-developed research on these issues. This research includes, for example, analysis of large-scale integration in aircraft design; comprehensive analyses of symphonies and paintings; grammars for design (e.g., in architecture, structural engineering, computer programming, manufacturing); classification systems for ethnic artifacts; problem reformulation in AI; aesthetically powerful models in astrophysics; systematizations of mathematical crystallography and their application to design; cohomological unification in quantum mechanics, etc.

The society is a division of the INTERNATIONAL SOCIETY FOR GROUP THEORY IN COGNITIVE SCIENCE: For more information contact: Professor Michael Leyton, Center for Discrete Mathematics & Theoretical Computer Science (DIMACS), Rutgers University: