Bastien has composed music for Dominique Bagouet’s ballets, and it was for his Tartine production that he made his first musical machine, combining a record-playing engine, a Meccano structure and a cymbal. The products of a strange cross between modern technology and ethnic folklore, his works are reminiscent of futurist primitivism and dadaism. In the words of Marc Gabriel Malfant, the music of Pierre Bastien has also rediscovered the pure charm of ‘air’ or tune, the easy-to-whistle-to genre pursued by une, the easy-to-whistle-to genre pursued by Bach that has disappeared from the musical vocabulary.
We enter, through music, into a forgotten world where tired machines slowly and obstinately repeat coagulated tunes. The tempo is heavy, decomposed. In this nocturnal milieu, the apparitions have the mysterious walk of the ghosts and their power of fascination. These ‘airs’ have the elegance of a remembrance… And sometimes, we surprise ourselves whistling a melody of Pierre Bastien while we maintain fixed in our memory the sorrowful calm of Marimba Combo’s cornet.
Outside In is a Mathematical Visualization Project from the Geometry Center. The video illustrates an amazing mathematical discovery made in 1957: you can turn the surface of a sphere inside out without making a hole, if you think of the surface as being made of an elastic material that can pass through itself. Communicating how this process of eversion can be carried out has been a challenge to differential topologists ever since.
“Outside In” uses nontechnical language and computer animation to illustrate the process and to explain the concepts involved to a nonmathematical audience. Yetthe video retains mathematical depth: we introduce the concept of a “regular homotopy” from topology, which is traditionally not encountered until advanced undergraduate mathematics classes. The metaphor we use is that of a material that can stretch and pass through itself, but that self-destructs if punctured or even pinched sharply. Of course, there is no such material in real life! That’s where computer graphics comes in.
The framework is a dialogue between a female teacher and a male student. In the first scene they work out between themselves the ground rules of what it means to turn a sphere inside out, but the student remains skeptical that the problem can be solved under these rules. If anything his skepticism
increases in subsequent scenes, as the teacher persuades him that a circle cannot be turned inside out underthe same rules. However, an idea that is introduced in connection with curves—namely, adding waves, or corrugations—turns out to be useful for surfaces as well. In the final scene of the twenty-minute movie, the student is shown how to turn the sphere inside out using this corrugation method. The process is shown a number of different ways to build up the student’s (and the viewer’s) intuition.