The Maggot in the Apple: Peaceful Coexistence of Incompatible Theories

In physics, as in science generally, most phenomena can be understood in more than one way: the gas in an engine obeys the laws of thermodynamics and also those of the motion of its molecules. The different theories correspond to different levels of description. These must overlap, but understanding their consilience is far from straightforward because they are usually based on seemingly incompatible concepts. The discordance arises from the fact, unappreciated until recently, that the limit in which the more general theory reduces to the less general (usually older) theory is mathematically singular. One consequence is a range of phenomena, of intense current interest, inhabiting the borderlands between the theories. I will explore this theme with examples from the physics of fluids, light and the quantum world.