Poohsticks and differential geometry

Pooh Sticks Bridge, Ashdown Forest. Image credit: David Brooker / geograph.org.uk

Poohsticks is a game whereby players drop sticks into a flowing river or stream, preferably from a bridge, and observe their motion. Poohsticks happens to also be a valuable teaching tool in differential geometry.

The flow of the stream defines a one-parameter (the parameter being time) family of diffeomorphisms (physically, only approximately so) of the surface of the stream to itself. Dropping a handful of (preferably small) sticks onto the stream surface marks a vector field on this surface. The sticks are carried by the surface flow. The rate of change of the sticks is then nothing but the Lie derivative of the stick vector field with respect to the flow field.

Willie WY Wong
Associate Professor

My research interests include partial differential equations, geometric analysis, fluid dynamics, and general relativity.