In physics, as in science generally, most phenomena can be understood in more than one way: the gas in an engine obeys not only the laws of thermodynamics but also those of the motion of its molecules.
The different theories correspond to different levels of description. These must overlap, but their consilience is far from straightforward because they seem based on incompatible concepts.
The discordance arises from the fact, appreciated in its generality only recently, that the limit in which the more encompassing 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.