Toy Models of Top Down Causation

Abstract: Models in which causation arises from higher level structures as well as from microdynamics may be relevant to unifying quantum theory with classical physics or general relativity. They also give a way of defining a form of panprotopsychist property dualism, in which consciousness and material physics causally affect one another. I describe toy models based on probabilistic cellular automata that illustrate possibilities and difficulties with these ideas.