In this Public Lecture, which contains more technical content than our norm, John Bush presents seemingly disparate topics which are in fact united by a common theme and underlaid by a common mathematical framework. First there is the natural world where creatures use surface tension to support themselves on the water surface and propel themselves along it. Then there is a small droplet bouncing along the surface of a vibrating liquid bath, guided or 'piloted’ by its own wave field - its ability to reproduce many features previously thought to be exclusive to quantum systems has launched the field of hydrodynamic quantum analogs, and motivated a critical revisitation of the philosophical foundations of quantum mechanics. John Bush is a Professor of Applied Mathematics in the Department of Mathematics at MIT specialising in fluid dynamics. The Oxford Mathematics Public Lectures are generously supported by XTX Markets.