Holonomy Blocks
An interactive installation, with Henry Segerman. An arrow slidesaround a closed path on three carved wooden surfaces.
Made with Henry Segerman and exhibited at the Warped Realities: The Art of Differential Geometry exhibition at the Museum of Mathematics (MoMath), New York, 2025 and the ICM, 2026.
Three CNC-carved wooden surfaces sit side by side: a sphere (positive curvature), a flat plane (zero curvature), and a saddle (negative curvature). Each surface was carved from cherry wood on a CNC router, with channels routed to guide a sliding arrow along the surface, in parallel transport.
A metal arrow slides freely along rails fitted into those channels. The arrow rests on four ball bearings so it traverses the surface without twisting in its own plane, taking the right angles corners using its own symmetry.
When the arrow completes a loop on the right-angled track on the flat surface it points the same way on return. On the sphere or saddle the arrow comes back rotated, even though it was never twisted in place. The journey caused the rotation.
This effect is holonomy. The angle through which the arrow turns reveals the curvature of the surface, related by the Gauss-Bonnet theorem. The three surfaces make this comparison immediate and tactile: positive curvature produces a rotation in one direction, negative curvature the other, and the flat plane none at all.
