Experiential Braid Relations on display in Providence, RI, August 2025
Dimensions: One box: 16.0 x 12.0 x 5.0 cm. Assembled tower: 16.0 x 24.0 x 6 cm.
Materials: Laser cut wood, Optical Cable, 3D printed parts, LED lights, and magnets.
Experiential Braid Relations is an interactive light display that explores the structure of the permutation group S4. A group element is visualized by a permutation of five colors. Each box is a conduit that permutes the input colors according to a predefined permutation. Viewers build towers of boxes to explore multiplication of permutations. Viewers can discern that permutation multiplication is not commutative, that every permutation is the product of adjacent transpositions, and that adjacent transpositions satisfy the expected braid relations. Engravings on the boxes provide for a "beginner mode" in which viewers can be guided by the braid relations, and an "advanced mode" in which viewers use their permutation multiplication skills.
Exhibited at the 2025 Bridges Conference in Eindhoven, NL and at ICERM in Providence, RI
Experiential Braid Relations on display in Eindhoven, NL, July 2025
