Change the current, or push the boat: both send it through the same side opening. This allegory compares outcomes, not identical paths or a proof of duality.
Settings, scope and source files
A straight main channel and a separate side spillway. In the stated 2D model, the unperturbed boat passes the side opening; increasing the inflow or pushing with a pole sends it out through that opening. The three scenes share the same initial boat state and physical time scale. Sharing an outlet does not imply identical trajectories or prove a mathematical duality. Upstream transport, watercolor texture, gate egress, and falling-water optics are illustrative; spatial convergence for the final configuration has not been established.
Animation plays automatically · reduced motion keeps a still frame